Exploring potential associations between childhood undernutrition and the Standardized Precipitation Evapotranspiration Index (SPEI) in Brazilian municipalities (2008–2019)
Overview
This report explores potential associations between childhood undernutrition and the Standardized Precipitation Evapotranspiration Index (SPEI) in Brazilian municipalities (2008–2019). It is part of the Sustentarea Research and Extension Group’s project titled Global syndemic: The impact of anthropogenic climate change on the health and nutrition of children under five years old served by Brazil’s public health system (SUS).
Please note that this report is designed to support decision-making and may not include all the details of the analysis.
Methods
Approach and Procedure Method
The analysis was conducted using Generalized Additive Models (GAMs) to model and control for potential effects, alongside visual inspections of the data. Results are also presented for each cluster of the Revised Multidimensional Index for Sustainable Food Systems (MISFS-R) (Carvalho et al., 2021; Norde et al., 2023).
Any additional analyses or updates will be incorporated into this report in future revisions, if necessary.
Source of Data/Information
The data used in this analysis have as sources:
- The Brazilian Institute of Geography and Statistics (IBGE) Automatic Retrieval System (SIDRA), for data on GDP per capita.
- Brazil’s Food and Nutrition Surveillance System (SISVAN), for data on malnutrition.
- WorldClim, for data on bioclimatic variables, which allowed us to calculate the Standardised Precipitation Evapotranspiration Index (SPEI) for municipalities in Brazil.
Some of the data are embedded in the document, while others rely on external data files available in the data directory of the code repository.
Data Wrangling
Data wrangling and analysis followed the data science framework outlined by Wickham et al. (2023), as illustrated in Figure 1. All processes were made using the R programming language (R Core Team, n.d.), RStudio IDE (Posit Team, n.d.), and several R packages.
The tidyverse and rOpenSci peer-reviewed package ecosystem and other R packages adherents of the tidy tools manifesto (Wickham et al., 2023) were prioritized. All processes were made in order to provide result reproducibility and to be in accordance with the FAIR principles (Wilkinson et al., 2016).
Source: Reproduced from Wickham et al. (2023).
The Tidyverse code style guide and design principles were followed to ensure consistency and enhance readability.
All the analyses are 100% reproducible and can be run again at any time. See the README file in the code repository to learn how to run them.
Model Parameters
The models were built using the mgcv R package (Wood, n.d.). Since the dependent variables are relative frequencies (continuous), we used the beta distribution family (Figure 2) with a logit link function (Equation 1)(Figure 3)(see Casella & Berger (2002)[p. 591). The REML (Restricted Maximum Likelihood) method was used to estimate the smoothing parameters.
Code
list <-
dplyr::tibble(
alpha = c(0.5, 5, 1, 2, 2),
beta = c(0.5, 1, 3, 2, 5),
color = c(
"a = b == 0.5",
"a = 5, b = 1",
"a = 1, b = 3",
"a = 2, b = 2",
"a = 2, b = 5"
)
) %>%
split(., seq(nrow(.)))
plot <-
ggplot2::ggplot(NULL, ggplot2::aes(x = x, color = color)) +
ggplot2::labs(
x = "x",
y = "Probability Density Function (PDF)",
color = "Parameters"
) +
ggplot2::scale_y_continuous(limits = c(0, 2.5))+
scale_color_brand_d()
for (i in list) {
plot <-
plot +
ggplot2::stat_function(
data = dplyr::tibble(x = 0:1, color = factor(i$color)),
fun = stats::dbeta,
args = list(shape1 = i$alpha, shape2 = i$beta),
n = 1000,
linewidth = 1.5
)
}
plot |> print() |> rutils::shush()Source: Created by the authors.
\[ \text{logit}(P) = \ln\left(\frac{P}{1 - P}\right) = \beta_{0} + \beta_{1} X_{1} + \cdots + \beta_{k} X_{k} \tag{1}\]
Code
ggplot2::ggplot() +
ggplot2::stat_function(
data = dplyr::tibble(x = 0:1, color = factor(i$color)),
fun = stats::qlogis,
args = list(location = 0, scale = 1, log = FALSE),
n = 1000,
linewidth = 1.5,
color = get_brand_color("red")
) +
ggplot2::geom_hline(
yintercept = 0,
linewidth = 0.25,
linetype = "dashed",
color = get_brand_color("grey")
) +
ggplot2::geom_vline(
xintercept = 0.5,
linewidth = 0.25,
linetype = "dashed",
color = get_brand_color("grey")
) +
ggplot2::lims(
x = c(0, 1),
y = c(-6, 6)
) +
ggplot2::labs(
x = "Probability",
y = "Logit(0,1)"
)Interpretation of Results
Standardized Precipitation Evapotranspiration Index (SPEI)
Since the original SPEI authors (Vicente-Serrano et al., 2010) did not establish definitive thresholds for SPEI values and their corresponding drought conditions, we adopt the benchmark values provided by Mehr et al. (2020) (Table 1).
| Classification | SPI Threshold | SPEI Threshold |
|---|---|---|
| Extremely wet | 2.0 ≤ SPI | 1.83 ≤ SPEI |
| Severely wet | 2.0 > SPI ≥ 1.5 | 1.82 > SPEI ≥ 1.43 |
| Moderately wet | 1.49 > SPI ≥ 1.0 | 1.42 > SPEI ≥ 1.0 |
| Near normal | -1.0 ≤ SPI ≤ 1.0 | -1.0 ≤ SPEI ≤ 1.0 |
| Moderate drought (MoD) | -1.49 ≤ SPI < -1.0 | -1.42 ≤ SPEI < -1.0 |
| Severe drought (SD) | -2.0 ≤ SPI < -1.5 | -1.82 ≤ SPEI < -1.43 |
| Extreme drought (ED) | SPI < -2.0 | SPEI < -1.83 |
Source: Reproduced from Mehr et al. (2020).
Revised Multidimensional Index for Sustainable Food Systems (MISFS-R)
The Multidimensional Index for Sustainable Food Systems (MISFS) is a tool designed to measure the sustainability of food systems at a subnational level, specifically created for Brazil, taking into account local behaviours and practices. The MISFS-R is a revised version of the MISFS, which includes new indicators and a new methodology for calculating the index Figure 4. See Carvalho et al. (2021) and Norde et al. (2023) to learn more.
Source: Reproduced from Norde et al. (2023).
Pratical Significance
To ensure practical significance, the adjusted \(\text{R}^2\) of the models are analysed for their effect sizes considering a confidence interval of \(0.95\). We use Cohen (1988) benchmark for interpretation.
A \(\text{R}^2\) less than \(\approx 0.0196\) is considered negligeble.
SMALL EFFECT SIZE: \(f^2 = .02\). Translated into \(\text{R}^{2}\) or partial \(\text{R}^{2}\) for Case 1, this gives \(.02 / (1 + .02) = .0196\). We thus define a small effect as one that accounts for 2% of the \(\text{Y}\) variance (in contrast with 1% for \(r\)), and translate to an \(\text{R} = \sqrt{0196} = .14\) (compared to .10 for \(r\)). This is a modest enough amount, just barely escaping triviality and (alas!) all too frequently in practice represents the true order of magnitude of the effect being tested (Cohen, 1988, p. 413).
[…] in many circumstances, all that is intended by “proving” the null hypothesis is that the ES [Effect Size] is not necessarily zero but small enough to be negligible […]. (Cohen, 1988, p. 461).
Setting the Enviroment
Code
library(beepr)
library(broom)
library(cli)
library(clipr)
library(colorspace)
library(dplyr)
library(effectsize)
library(GGally)
library(geobr)
library(ggplot2)
library(ggspatial)
library(glmmTMB)
library(here)
library(janitor)
library(lme4)
library(lubridate)
library(lubritime) # github.com/danielvartan/lubritime
library(magrittr)
library(mgcv)
library(mgcViz)
library(MuMIn)
library(pal) # gitlab.com/rpkg.dev/pal
library(patchwork)
library(performance)
library(polyglotr)
library(prettycheck) # github.com/danielvartan/prettycheck
library(psychometric)
library(purrr)
library(r2glmm)
library(ragg)
library(RColorBrewer)
library(readr)
library(readxl)
library(rutils) # github.com/danielvartan/rutils
library(sidrar)
library(stats)
library(stringr)
library(summarytools)
library(tidyr)Code
source(here::here("R", "get_and_aggregate_sidra_by_year.R"))
source(here::here("R", "gam_misfs.R"))
source(here::here("R", "plot_brazil.R"))
source(here::here("R", "plot_dist.R"))
source(here::here("R", "plot_gam.R"))
source(here::here("R", "plot_ggally.R"))
source(here::here("R", "summarise_coefs.R"))
source(here::here("R", "summarise_r2.R"))
source(here::here("R", "tabset_panel_brazil_municipality.R"))
source(here::here("R", "tabset_panel_gam.R"))
source(here::here("R", "tabset_panel_var_distribution.R"))
source(here::here("R", "tabset_panel_var_distribution_by_misfs.R"))
source(here::here("R", "utils.R"))
source(here::here("R", "utils-plots.R"))Importing and Tidying the Data
Nutrition Data
Based on SISVAN Nutritional Status dataset (Sistema de Vigilância Alimentar e Nutricional, n.d.).
Code
nutrition_data <-
here::here("data", "Banco_dados_malnutritio_clima - Adaptado.csv") |>
readr::read_csv(col_types = readr::cols(.default = "c")) |>
janitor::clean_names() |>
dplyr::rename(
year = ano,
municipality_code = code_muni,
sisvan_cover = cobrs,
number_of_children = n_ao_de_criana_as_municipio_x,
n_mbepr = muito_baixa_e_i_n_x,
n_beipr = baixa_e_i_n_x,
n_maper = magreza_acentuada_p_e_n_x,
n_mpepr = magreza_p_e_n_x
) |>
dplyr::select(
year, municipality_code, misf, number_of_children, sisvan_cover,
n_mbepr, n_beipr, n_maper, n_mpepr
) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::all_of(
c("number_of_children", "n_mbepr", "n_beipr", "n_maper", "n_mpepr")
),
.fns = ~
dplyr::case_when(
!(as.numeric(.x) %% 1 == 0) ~ stringr::str_remove(.x, "\\."),
TRUE ~ .x
) |>
as.integer()
)
) |>
dplyr::mutate(
# year = as.integer(year),
year =
year |>
factor(
levels = year |> unique() |> sort(),
ordered = TRUE
),
municipality_code = as.integer(municipality_code),
misf = factor(misf, levels = c("A", "B", "C", "D"), ordered = FALSE),
sisvan_cover = as.numeric(sisvan_cover),
mbepr = n_mbepr,
beipr = n_beipr,
n_mbepr_beipr = n_mbepr + n_beipr,
mbepr_beipr = n_mbepr_beipr,
maper = n_maper,
mpepr = n_mpepr,
n_maper_mpepr = n_maper + n_mpepr,
maper_mpepr = n_maper_mpepr
) |>
dplyr::filter(
dplyr::between(sisvan_cover, 0, 1),
number_of_children >= 0,
number_of_children > n_mbepr,
number_of_children > n_beipr,
number_of_children > mbepr_beipr,
number_of_children > n_maper,
number_of_children > n_mpepr,
number_of_children > maper_mpepr
) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::all_of(
c("mbepr", "beipr", "mbepr_beipr", "maper", "mpepr", "maper_mpepr")
),
.fns = ~
.x %>%
`/`(number_of_children * sisvan_cover)
),
dplyr::across(
.cols = dplyr::all_of(
c("mbepr", "beipr", "mbepr_beipr", "maper", "mpepr", "maper_mpepr")
),
.fns = ~ pmax(0.00001, pmin(.x, 0.99999))
)
) |>
dplyr::select(
year, municipality_code, misf, number_of_children, sisvan_cover,
n_mbepr, mbepr, n_beipr, beipr, n_mbepr_beipr, mbepr_beipr,
n_maper, maper, n_mpepr, mpepr, n_maper_mpepr, maper_mpepr
)GDP Per Capita Data
Source: IBGE-SIDRA Table 5938 – Gross domestic product at current prices, taxes net of subsidies on products at current prices, and gross value added at current prices, total and by economic activity, and their respective shares - Reference year 2010 (Instituto Brasileiro de Geografia e Estatística, n.d.-a).
Source: IBGE-SIDRA Table 6579 – Estimated resident population (Instituto Brasileiro de Geografia e Estatística, n.d.-b).
Code
gdp_data <-
ibge_table_5938 |>
dplyr::left_join(
ibge_table_6579,
by = c("year", "municipality_code")
) |>
dplyr::select(year, municipality_code, municipality.x, value.x, value.y) |>
dplyr::rename(
gdp = value.x,
population = value.y,
municipality = municipality.x
) |>
dplyr::filter(gdp >= 0, population >= 0) |>
dplyr::mutate(
# year = as.integer(year),
year =
year |>
factor(
levels = year |> unique() |> sort(),
ordered = TRUE
),
gdp = gdp * 1000,
gdp_per_capita = gdp / population,
municipality_code = municipality_code |> as.integer()
)SPEI Data
Based on WorldClim 2.1 Historical Monthly Weather dataset (Fick & Hijmans, 2017; Harris et al., 2020).
Code
spei_data <-
here::here("data", "spei_Extreme_drought_event_municipality_year2.csv") |>
readr::read_csv(col_types = readr::cols(.default = "c")) |>
janitor::clean_names() |>
dplyr::rename(municipality_code = code_muni) |>
dplyr::select(
municipality_code,
dplyr::all_of(paste0("spei_12m_", nutrition_data$year |> unique()))
) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::starts_with("spei_12m"),
.fns = as.numeric
)
) |>
tidyr::pivot_longer(
cols = starts_with("spei_12m"),
names_to = "year",
values_to = "spei_12m"
) |>
dplyr::mutate(
year =
year |>
stringr::str_remove("spei_12m_") |>
as.integer(),
year =
year |>
factor(
levels = year |> unique() |> sort(),
ordered = TRUE
),
municipality_code = municipality_code |> as.integer()
)Analysis Data
Code
data <-
nutrition_data |>
dplyr::mutate(year = year |> as.character()) |>
# In order to adapt the data to the municipalities in the nutrition data
# since it does not have the check digit.
dplyr::rename(temp_municipality_code = municipality_code) |>
dplyr::left_join(
y = gdp_data |>
dplyr::mutate(
year = year |> as.character(),
temp_municipality_code =
municipality_code |>
stringr::str_sub(end = -2) |>
as.integer()
),
by = c("year", "temp_municipality_code")
) |>
dplyr::left_join(
y = spei_data |>
dplyr::mutate(
year = year |> as.character(),
# In order to adapt the data to the municipalities
# in the nutrition data (...)
temp_municipality_code =
municipality_code |>
stringr::str_sub(end = -2) |>
as.integer()
),
by = c("year", "temp_municipality_code")
) |>
dplyr::rename(municipality_code = municipality_code.x) |>
dplyr::select(
year, municipality_code, misf, number_of_children, sisvan_cover,
mbepr, beipr, mbepr_beipr, maper, mpepr, maper_mpepr,
gdp_per_capita, spei_12m
) |>
dplyr::mutate(
# year = as.integer(year),
year =
year |>
factor(
levels = year |> unique() |> sort(),
ordered = TRUE
)
) |>
tidyr::drop_na(sisvan_cover)Code
dplyr::tibble(
n = data |> nrow(),
n_sisvan_cover_less_than_0_05 =
data |>
dplyr::filter(sisvan_cover < 0.05) |>
nrow(),
n_sisvan_cover_more_than_1 =
data |>
dplyr::filter(sisvan_cover > 1) |>
nrow(),
n_brazil_municipalities =
geobr::read_municipality(year = 2022, showProgress = FALSE) |>
dplyr::pull(code_muni) |>
length() |>
rutils::shush(),
missing_municipalities =
geobr::read_municipality(year = 2022, showProgress = FALSE) |>
dplyr::pull(code_muni) |>
as.integer() |>
setdiff(data |> dplyr::pull(municipality_code)) |>
length() |>
rutils::shush()
) |>
tidyr::pivot_longer(cols = dplyr::everything())Adjusting the data to allow only municipalities with a minimum of \(5\%\) cover from SISVAN.
Code
data <-
data |>
dplyr::filter(sisvan_cover >= 0.05)
dataDictionary
-
year: Year of data collection. -
municipality_code: Brazilian Institute of Geography and Statistics (IBGE) municipality code. -
misf: Cluster of the Revised Multidimensional Index for Sustainable Food Systems (MISFS-R) (A, B, C, or D). -
number_of_children: Number of children under five years old in the municipality. -
sisvan_cover: Proportion of children under five covered by the Brazilian Food and Nutrition Surveillance System (SISVAN) in the municipality. -
mbepr: Relative frequency of children under five years old with Very Short Stature for Age (Muito Baixa Estatura Para a Idade) in the municipality. -
beipr: Relative frequency of children under five years old with Short Stature for Age (Baixa Estatura Para Idade) in the municipality. -
mbepr_beipr: Relative frequency of children under five years old with Very Short/Short Stature for Age (Muito Baixa/Baixa Estatura Para Idade) in the municipality. -
maper: Relative frequency of children under five years old with Severe Thinness for Height (Magreza Acentuada Para a Estatura) in the municipality. -
mpepr: Relative frequency of children under five years old with Thinness for Height (Magreza Por Estatura) in the municipality. -
maper_mpepr: Relative frequency of children under five years old with Severe/Moderate Thinness for Height (Magreza Acentuada/Moderada Para a Estatura) in the municipality. -
gdp_per_capita: Gross Domestic Product (GDP) per capita in the municipality in Brazilian Reais (BRL). -
spei_12m: Standardised Precipitation Evapotranspiration Index (SPEI) in a 12-month times cale for the municipality.
Checking SISVAN Cover
Code
brand_div_palette <- function(x) {
make_color_vector(
n_prop = x,
colors = c(
get_brand_color("dark-red"),
# get_brand_color("white"),
get_brand_color_mix(
position = 950,
color_1 = "dark-red",
color_2 = "dark-red-triadic-blue",
alpha = 0.5
),
get_brand_color("dark-red-triadic-blue")
)
)
}Code
# Run this chunk to produce the plots and the animation.
data |>
dplyr::mutate(sisvan_cover = sisvan_cover * 100) |>
animate_plot_brazil_municipality(
col_fill = "sisvan_cover",
col_group = "year",
group_label = "Year",
comparable_areas = TRUE
suffix = NULL,
width = 1344,
height = 960,
dpi = 150,
transform = "identity",
breaks = seq(0, 100, 25),
reverse = FALSE,
limits = c(0, 100),
palette = brand_div_palette
)Checking SPEI Variations
Year-to-Year comparison
Code
# Run this chunk to produce the plots and the animation.
data |>
animate_plot_brazil_municipality(
col_fill = "spei_12m",
col_group = "year",
group_label = "Year",
comparable_areas = TRUE
suffix = NULL,
width = 1344,
height = 960,
dpi = 150,
transform = "identity",
# breaks = c(-2, -1.83, -1.43, -1, 1, 1.42, 1.82, 2),
breaks = seq(-2 , 2, 0.5),
reverse = FALSE,
limits = c(-2, 2),
palette = brand_div_palette
)Source: Created by the authors using data from the WorldClim 2.1 Historical Monthly Weather dataset (Fick & Hijmans, 2017; Harris et al., 2020).
Source: Created by the authors using data from the WorldClim 2.1 Historical Monthly Weather dataset (Fick & Hijmans, 2017; Harris et al., 2020).
Source: Created by the authors using data from the WorldClim 2.1 Historical Monthly Weather dataset (Fick & Hijmans, 2017; Harris et al., 2020).
Source: Created by the authors using data from the WorldClim 2.1 Historical Monthly Weather dataset (Fick & Hijmans, 2017; Harris et al., 2020).
Source: Created by the authors using data from the WorldClim 2.1 Historical Monthly Weather dataset (Fick & Hijmans, 2017; Harris et al., 2020).
Source: Created by the authors using data from the WorldClim 2.1 Historical Monthly Weather dataset (Fick & Hijmans, 2017; Harris et al., 2020).
Source: Created by the authors using data from the WorldClim 2.1 Historical Monthly Weather dataset (Fick & Hijmans, 2017; Harris et al., 2020).
Source: Created by the authors using data from the WorldClim 2.1 Historical Monthly Weather dataset (Fick & Hijmans, 2017; Harris et al., 2020).
Source: Created by the authors using data from the WorldClim 2.1 Historical Monthly Weather dataset (Fick & Hijmans, 2017; Harris et al., 2020).
Source: Created by the authors using data from the WorldClim 2.1 Historical Monthly Weather dataset (Fick & Hijmans, 2017; Harris et al., 2020).
Source: Created by the authors using data from the WorldClim 2.1 Historical Monthly Weather dataset (Fick & Hijmans, 2017; Harris et al., 2020).
Source: Created by the authors using data from the WorldClim 2.1 Historical Monthly Weather dataset (Fick & Hijmans, 2017; Harris et al., 2020).
Source: Created by the authors using data from the WorldClim 2.1 Historical Monthly Weather dataset (Fick & Hijmans, 2017; Harris et al., 2020).
Comparison with External Data
Figure 31 presents an independent analysis for comparison, while our results are shown in Figure 32.
Source: Reproduced from Food and Agriculture Organization of the United Nations et al. (2025, fig. VI.1, p. 185).
Code
plot <-
data |>
dplyr::filter(year >= 2010, year <= 2019) |>
plot_brazil_municipality(
col_fill = "spei_12m",
comparable_areas = TRUE,
transform = "identity",
binned = FALSE,
breaks = seq(-2 , 2, 0.5),
reverse = FALSE,
limits = c(-2, 2),
print = FALSE,
quiet = TRUE,
palette = function(x) {
make_color_vector(
n_prop = x,
colors = c(
"#6F0322",
"#BC2D32",
"#E28668",
"#F9D0BC",
"#F1F1F3",
"#BBDAE9",
"#65A9D1",
"#266DB1",
"#0D2648"
)
)
}
) +
ggplot2::labs(title = "2010-2019") +
ggplot2::theme(plot.title = element_text(hjust = 0.5))
plot |> print() |> rutils::shush()Source: Created by the authors using data from the WorldClim 2.1 Historical Monthly Weather dataset (Fick & Hijmans, 2017; Harris et al., 2020).
Checking Distributions
General Distributions
Code
data |>
summarytools::freq(
var = year,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)year variable.
| Freq | % Valid | % Valid Cum. | % Total | % Total Cum. | |
|---|---|---|---|---|---|
| 2008 | 4996 | 7.96 | 7.96 | 7.96 | 7.96 |
| 2009 | 5253 | 8.37 | 16.33 | 8.37 | 16.33 |
| 2010 | 5274 | 8.40 | 24.73 | 8.40 | 24.73 |
| 2011 | 5266 | 8.39 | 33.12 | 8.39 | 33.12 |
| 2012 | 5288 | 8.43 | 41.55 | 8.43 | 41.55 |
| 2013 | 5143 | 8.19 | 49.74 | 8.19 | 49.74 |
| 2014 | 5164 | 8.23 | 57.97 | 8.23 | 57.97 |
| 2015 | 5229 | 8.33 | 66.30 | 8.33 | 66.30 |
| 2016 | 5280 | 8.41 | 74.72 | 8.41 | 74.72 |
| 2017 | 5263 | 8.39 | 83.10 | 8.39 | 83.10 |
| 2018 | 5271 | 8.40 | 91.50 | 8.40 | 91.50 |
| 2019 | 5335 | 8.50 | 100.00 | 8.50 | 100.00 |
| <NA> | 0 | 0.00 | 100.00 | ||
| Total | 62762 | 100.00 | 100.00 | 100.00 | 100.00 |
Source: Created by the authors.
Code
data |>
plot_bar(
col = "year",
y_label = "year"
)Code
data |>
summarytools::freq(
var = misf,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)misf variable.
| Freq | % Valid | % Valid Cum. | % Total | % Total Cum. | |
|---|---|---|---|---|---|
| A | 7934 | 12.64 | 12.64 | 12.64 | 12.64 |
| B | 31734 | 50.56 | 63.20 | 50.56 | 63.20 |
| C | 20324 | 32.38 | 95.59 | 32.38 | 95.59 |
| D | 2770 | 4.41 | 100.00 | 4.41 | 100.00 |
| <NA> | 0 | 0.00 | 100.00 | ||
| Total | 62762 | 100.00 | 100.00 | 100.00 | 100.00 |
Source: Created by the authors.
Code
data |>
plot_bar(
col = "misf",
y_label = "misf"
)Code
data |>
summarytools::descr(
var = number_of_children,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)number_of_children variable.
| number_of_children | |
|---|---|
| Mean | 2498.50 |
| Std.Dev | 9764.47 |
| Min | 41.00 |
| Q1 | 399.00 |
| Median | 910.00 |
| Q3 | 2009.00 |
| Max | 797644.00 |
| MAD | 911.80 |
| IQR | 1610.00 |
| CV | 3.91 |
| Skewness | 32.79 |
| SE.Skewness | 0.01 |
| Kurtosis | 1888.84 |
| N.Valid | 62762.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data |>
plot_dist(
col = "number_of_children",
jitter = FALSE
)Code
data |>
summarytools::descr(
var = sisvan_cover,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)sisvan_cover variable.
| sisvan_cover | |
|---|---|
| Mean | 0.41 |
| Std.Dev | 0.23 |
| Min | 0.05 |
| Q1 | 0.23 |
| Median | 0.38 |
| Q3 | 0.57 |
| Max | 1.00 |
| MAD | 0.25 |
| IQR | 0.34 |
| CV | 0.55 |
| Skewness | 0.51 |
| SE.Skewness | 0.01 |
| Kurtosis | -0.55 |
| N.Valid | 62762.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data |>
plot_dist(
col = "sisvan_cover",
jitter = FALSE
)Code
data |>
summarytools::descr(
var = mbepr,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)mbepr variable.
| mbepr | |
|---|---|
| Mean | 0.06 |
| Std.Dev | 0.05 |
| Min | 0.00 |
| Q1 | 0.03 |
| Median | 0.05 |
| Q3 | 0.07 |
| Max | 0.89 |
| MAD | 0.03 |
| IQR | 0.04 |
| CV | 0.81 |
| Skewness | 3.16 |
| SE.Skewness | 0.01 |
| Kurtosis | 23.36 |
| N.Valid | 62762.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data |>
plot_dist(
col = "mbepr",
jitter = FALSE
)Code
data |>
summarytools::descr(
var = beipr,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)beipr variable.
| beipr | |
|---|---|
| Mean | 0.07 |
| Std.Dev | 0.04 |
| Min | 0.00 |
| Q1 | 0.04 |
| Median | 0.06 |
| Q3 | 0.08 |
| Max | 0.69 |
| MAD | 0.03 |
| IQR | 0.04 |
| CV | 0.54 |
| Skewness | 1.42 |
| SE.Skewness | 0.01 |
| Kurtosis | 5.80 |
| N.Valid | 62762.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data |>
plot_dist(
col = "beipr",
jitter = FALSE
)Code
data |>
summarytools::descr(
var = mbepr_beipr,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)mbepr_beipr variable.
| mbepr_beipr | |
|---|---|
| Mean | 0.12 |
| Std.Dev | 0.07 |
| Min | 0.00 |
| Q1 | 0.08 |
| Median | 0.11 |
| Q3 | 0.15 |
| Max | 1.00 |
| MAD | 0.06 |
| IQR | 0.08 |
| CV | 0.58 |
| Skewness | 1.77 |
| SE.Skewness | 0.01 |
| Kurtosis | 6.89 |
| N.Valid | 62762.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data |>
plot_dist(
col = "mbepr_beipr",
jitter = FALSE
)Code
data |>
summarytools::descr(
var = maper,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)maper variable.
| maper | |
|---|---|
| Mean | 0.02 |
| Std.Dev | 0.03 |
| Min | 0.00 |
| Q1 | 0.01 |
| Median | 0.02 |
| Q3 | 0.03 |
| Max | 0.75 |
| MAD | 0.02 |
| IQR | 0.02 |
| CV | 1.05 |
| Skewness | 5.34 |
| SE.Skewness | 0.01 |
| Kurtosis | 68.42 |
| N.Valid | 62762.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data |>
plot_dist(
col = "maper",
jitter = FALSE
)Code
data |>
summarytools::descr(
var = mpepr,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)mpepr variable.
| mpepr | |
|---|---|
| Mean | 0.03 |
| Std.Dev | 0.02 |
| Min | 0.00 |
| Q1 | 0.02 |
| Median | 0.03 |
| Q3 | 0.04 |
| Max | 0.58 |
| MAD | 0.02 |
| IQR | 0.02 |
| CV | 0.67 |
| Skewness | 2.14 |
| SE.Skewness | 0.01 |
| Kurtosis | 23.16 |
| N.Valid | 62762.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data |>
plot_dist(
col = "mpepr",
jitter = FALSE
)Code
data |>
summarytools::descr(
var = maper_mpepr,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)maper_mpepr variable.
| maper_mpepr | |
|---|---|
| Mean | 0.05 |
| Std.Dev | 0.04 |
| Min | 0.00 |
| Q1 | 0.03 |
| Median | 0.05 |
| Q3 | 0.07 |
| Max | 0.91 |
| MAD | 0.03 |
| IQR | 0.04 |
| CV | 0.73 |
| Skewness | 3.14 |
| SE.Skewness | 0.01 |
| Kurtosis | 27.23 |
| N.Valid | 62762.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data |>
plot_dist(
col = "maper_mpepr",
jitter = FALSE
)Code
data |>
summarytools::descr(
var = gdp_per_capita,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)gdp_per_capita variable.
| gdp_per_capita | |
|---|---|
| Mean | 18045.58 |
| Std.Dev | 20454.91 |
| Min | 301.61 |
| Q1 | 7485.60 |
| Median | 12703.63 |
| Q3 | 22238.03 |
| Max | 815697.80 |
| MAD | 9267.71 |
| IQR | 14751.90 |
| CV | 1.13 |
| Skewness | 8.75 |
| SE.Skewness | 0.01 |
| Kurtosis | 179.42 |
| N.Valid | 57487.00 |
| Pct.Valid | 91.60 |
Source: Created by the authors.
Code
data |>
plot_dist(
col = "gdp_per_capita",
jitter = FALSE
)Code
data |>
summarytools::descr(
var = spei_12m,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)spei_12m variable.
| spei_12m | |
|---|---|
| Mean | -0.18 |
| Std.Dev | 0.41 |
| Min | -1.75 |
| Q1 | -0.48 |
| Median | -0.17 |
| Q3 | 0.11 |
| Max | 1.03 |
| MAD | 0.44 |
| IQR | 0.59 |
| CV | -2.27 |
| Skewness | -0.08 |
| SE.Skewness | 0.01 |
| Kurtosis | -0.44 |
| N.Valid | 62762.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data |>
plot_dist(
col = "spei_12m",
jitter = FALSE
)By MISFS-R Clusters
A
Code
data_misfs_a |>
summarytools::freq(
var = year,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)year variable.
| Freq | % Valid | % Valid Cum. | % Total | % Total Cum. | |
|---|---|---|---|---|---|
| 2008 | 615 | 7.75 | 7.75 | 7.75 | 7.75 |
| 2009 | 662 | 8.34 | 16.10 | 8.34 | 16.10 |
| 2010 | 663 | 8.36 | 24.45 | 8.36 | 24.45 |
| 2011 | 666 | 8.39 | 32.85 | 8.39 | 32.85 |
| 2012 | 665 | 8.38 | 41.23 | 8.38 | 41.23 |
| 2013 | 667 | 8.41 | 49.63 | 8.41 | 49.63 |
| 2014 | 670 | 8.44 | 58.08 | 8.44 | 58.08 |
| 2015 | 669 | 8.43 | 66.51 | 8.43 | 66.51 |
| 2016 | 663 | 8.36 | 74.87 | 8.36 | 74.87 |
| 2017 | 662 | 8.34 | 83.21 | 8.34 | 83.21 |
| 2018 | 663 | 8.36 | 91.57 | 8.36 | 91.57 |
| 2019 | 669 | 8.43 | 100.00 | 8.43 | 100.00 |
| <NA> | 0 | 0.00 | 100.00 | ||
| Total | 7934 | 100.00 | 100.00 | 100.00 | 100.00 |
Source: Created by the authors.
Code
data_misfs_a |>
plot_bar(
col = "year",
y_label = "year"
)Code
data_misfs_a |>
summarytools::descr(
var = number_of_children,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)number_of_children variable.
| number_of_children | |
|---|---|
| Mean | 1877.77 |
| Std.Dev | 5272.84 |
| Min | 59.00 |
| Q1 | 325.00 |
| Median | 682.50 |
| Q3 | 1554.00 |
| Max | 94954.00 |
| MAD | 651.60 |
| IQR | 1228.50 |
| CV | 2.81 |
| Skewness | 9.42 |
| SE.Skewness | 0.03 |
| Kurtosis | 117.89 |
| N.Valid | 7934.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data_misfs_a |>
plot_dist(
col = "number_of_children",
jitter = FALSE
)Code
data_misfs_a |>
summarytools::descr(
var = sisvan_cover,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)sisvan_cover variable.
| sisvan_cover | |
|---|---|
| Mean | 0.34 |
| Std.Dev | 0.18 |
| Min | 0.05 |
| Q1 | 0.20 |
| Median | 0.30 |
| Q3 | 0.44 |
| Max | 1.00 |
| MAD | 0.16 |
| IQR | 0.24 |
| CV | 0.54 |
| Skewness | 0.98 |
| SE.Skewness | 0.03 |
| Kurtosis | 0.79 |
| N.Valid | 7934.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data_misfs_a |>
plot_dist(
col = "sisvan_cover",
jitter = FALSE
)Code
data_misfs_a |>
summarytools::descr(
var = mbepr,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)mbepr variable.
| mbepr | |
|---|---|
| Mean | 0.06 |
| Std.Dev | 0.05 |
| Min | 0.00 |
| Q1 | 0.03 |
| Median | 0.05 |
| Q3 | 0.08 |
| Max | 0.78 |
| MAD | 0.03 |
| IQR | 0.04 |
| CV | 0.79 |
| Skewness | 3.77 |
| SE.Skewness | 0.03 |
| Kurtosis | 33.23 |
| N.Valid | 7934.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data_misfs_a |>
plot_dist(
col = "mbepr",
jitter = FALSE
)Code
data_misfs_a |>
summarytools::descr(
var = beipr,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)beipr variable.
| beipr | |
|---|---|
| Mean | 0.07 |
| Std.Dev | 0.04 |
| Min | 0.00 |
| Q1 | 0.04 |
| Median | 0.06 |
| Q3 | 0.08 |
| Max | 0.69 |
| MAD | 0.03 |
| IQR | 0.04 |
| CV | 0.56 |
| Skewness | 2.01 |
| SE.Skewness | 0.03 |
| Kurtosis | 16.06 |
| N.Valid | 7934.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data_misfs_a |>
plot_dist(
col = "beipr",
jitter = FALSE
)Code
data_misfs_a |>
summarytools::descr(
var = mbepr_beipr,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)mbepr_beipr variable.
| mbepr_beipr | |
|---|---|
| Mean | 0.13 |
| Std.Dev | 0.07 |
| Min | 0.00 |
| Q1 | 0.08 |
| Median | 0.11 |
| Q3 | 0.16 |
| Max | 1.00 |
| MAD | 0.06 |
| IQR | 0.08 |
| CV | 0.57 |
| Skewness | 2.25 |
| SE.Skewness | 0.03 |
| Kurtosis | 12.63 |
| N.Valid | 7934.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data_misfs_a |>
plot_dist(
col = "mbepr_beipr",
jitter = FALSE
)Code
data_misfs_a |>
summarytools::descr(
var = maper,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)maper variable.
| maper | |
|---|---|
| Mean | 0.03 |
| Std.Dev | 0.03 |
| Min | 0.00 |
| Q1 | 0.01 |
| Median | 0.02 |
| Q3 | 0.04 |
| Max | 0.59 |
| MAD | 0.02 |
| IQR | 0.02 |
| CV | 1.03 |
| Skewness | 5.40 |
| SE.Skewness | 0.03 |
| Kurtosis | 61.28 |
| N.Valid | 7934.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data_misfs_a |>
plot_dist(
col = "maper",
jitter = FALSE
)Code
data_misfs_a |>
summarytools::descr(
var = mpepr,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)mpepr variable.
| mpepr | |
|---|---|
| Mean | 0.03 |
| Std.Dev | 0.02 |
| Min | 0.00 |
| Q1 | 0.02 |
| Median | 0.03 |
| Q3 | 0.04 |
| Max | 0.46 |
| MAD | 0.02 |
| IQR | 0.02 |
| CV | 0.67 |
| Skewness | 2.53 |
| SE.Skewness | 0.03 |
| Kurtosis | 26.20 |
| N.Valid | 7934.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data_misfs_a |>
plot_dist(
col = "mpepr",
jitter = FALSE
)Code
data_misfs_a |>
summarytools::descr(
var = maper_mpepr,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)maper_mpepr variable.
| maper_mpepr | |
|---|---|
| Mean | 0.06 |
| Std.Dev | 0.04 |
| Min | 0.00 |
| Q1 | 0.04 |
| Median | 0.05 |
| Q3 | 0.08 |
| Max | 0.91 |
| MAD | 0.03 |
| IQR | 0.04 |
| CV | 0.71 |
| Skewness | 4.02 |
| SE.Skewness | 0.03 |
| Kurtosis | 41.22 |
| N.Valid | 7934.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data_misfs_a |>
plot_dist(
col = "maper_mpepr",
jitter = FALSE
)Code
data_misfs_a |>
summarytools::descr(
var = gdp_per_capita,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)gdp_per_capita variable.
| gdp_per_capita | |
|---|---|
| Mean | 22058.96 |
| Std.Dev | 20696.45 |
| Min | 3522.11 |
| Q1 | 11119.05 |
| Median | 16237.33 |
| Q3 | 25444.64 |
| Max | 362079.97 |
| MAD | 9273.49 |
| IQR | 14319.14 |
| CV | 0.94 |
| Skewness | 5.12 |
| SE.Skewness | 0.03 |
| Kurtosis | 47.82 |
| N.Valid | 7271.00 |
| Pct.Valid | 91.64 |
Source: Created by the authors.
Code
data_misfs_a |>
plot_dist(
col = "gdp_per_capita",
jitter = FALSE
)Code
data_misfs_a |>
summarytools::descr(
var = spei_12m,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)spei_12m variable.
| spei_12m | |
|---|---|
| Mean | -0.31 |
| Std.Dev | 0.41 |
| Min | -1.64 |
| Q1 | -0.60 |
| Median | -0.27 |
| Q3 | -0.03 |
| Max | 1.03 |
| MAD | 0.42 |
| IQR | 0.57 |
| CV | -1.31 |
| Skewness | -0.20 |
| SE.Skewness | 0.03 |
| Kurtosis | -0.31 |
| N.Valid | 7934.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data_misfs_a |>
plot_dist(
col = "spei_12m",
jitter = FALSE
)B
Code
data_misfs_b |>
summarytools::freq(
var = year,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)year variable.
| Freq | % Valid | % Valid Cum. | % Total | % Total Cum. | |
|---|---|---|---|---|---|
| 2008 | 2539 | 8.00 | 8.00 | 8.00 | 8.00 |
| 2009 | 2662 | 8.39 | 16.39 | 8.39 | 16.39 |
| 2010 | 2689 | 8.47 | 24.86 | 8.47 | 24.86 |
| 2011 | 2668 | 8.41 | 33.27 | 8.41 | 33.27 |
| 2012 | 2663 | 8.39 | 41.66 | 8.39 | 41.66 |
| 2013 | 2556 | 8.05 | 49.72 | 8.05 | 49.72 |
| 2014 | 2560 | 8.07 | 57.78 | 8.07 | 57.78 |
| 2015 | 2619 | 8.25 | 66.04 | 8.25 | 66.04 |
| 2016 | 2665 | 8.40 | 74.43 | 8.40 | 74.43 |
| 2017 | 2664 | 8.39 | 82.83 | 8.39 | 82.83 |
| 2018 | 2710 | 8.54 | 91.37 | 8.54 | 91.37 |
| 2019 | 2739 | 8.63 | 100.00 | 8.63 | 100.00 |
| <NA> | 0 | 0.00 | 100.00 | ||
| Total | 31734 | 100.00 | 100.00 | 100.00 | 100.00 |
Source: Created by the authors.
Code
data_misfs_b |>
plot_bar(
col = "year",
y_label = "year"
)Code
data_misfs_b |>
summarytools::descr(
var = number_of_children,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)number_of_children variable.
| number_of_children | |
|---|---|
| Mean | 2433.14 |
| Std.Dev | 11344.02 |
| Min | 41.00 |
| Q1 | 305.00 |
| Median | 647.00 |
| Q3 | 1627.00 |
| Max | 797644.00 |
| MAD | 644.93 |
| IQR | 1322.00 |
| CV | 4.66 |
| Skewness | 36.48 |
| SE.Skewness | 0.01 |
| Kurtosis | 1983.24 |
| N.Valid | 31734.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data_misfs_b |>
plot_dist(
col = "number_of_children",
jitter = FALSE
)Code
data_misfs_b |>
summarytools::descr(
var = sisvan_cover,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)sisvan_cover variable.
| sisvan_cover | |
|---|---|
| Mean | 0.38 |
| Std.Dev | 0.24 |
| Min | 0.05 |
| Q1 | 0.18 |
| Median | 0.32 |
| Q3 | 0.54 |
| Max | 1.00 |
| MAD | 0.24 |
| IQR | 0.36 |
| CV | 0.64 |
| Skewness | 0.74 |
| SE.Skewness | 0.01 |
| Kurtosis | -0.45 |
| N.Valid | 31734.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data_misfs_b |>
plot_dist(
col = "sisvan_cover",
jitter = FALSE
)Code
data_misfs_b |>
summarytools::descr(
var = mbepr,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)mbepr variable.
| mbepr | |
|---|---|
| Mean | 0.04 |
| Std.Dev | 0.04 |
| Min | 0.00 |
| Q1 | 0.02 |
| Median | 0.04 |
| Q3 | 0.06 |
| Max | 0.89 |
| MAD | 0.03 |
| IQR | 0.04 |
| CV | 0.94 |
| Skewness | 3.80 |
| SE.Skewness | 0.01 |
| Kurtosis | 32.09 |
| N.Valid | 31734.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data_misfs_b |>
plot_dist(
col = "mbepr",
jitter = FALSE
)Code
data_misfs_b |>
summarytools::descr(
var = beipr,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)beipr variable.
| beipr | |
|---|---|
| Mean | 0.06 |
| Std.Dev | 0.03 |
| Min | 0.00 |
| Q1 | 0.04 |
| Median | 0.05 |
| Q3 | 0.07 |
| Max | 0.49 |
| MAD | 0.02 |
| IQR | 0.03 |
| CV | 0.56 |
| Skewness | 1.45 |
| SE.Skewness | 0.01 |
| Kurtosis | 6.36 |
| N.Valid | 31734.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data_misfs_b |>
plot_dist(
col = "beipr",
jitter = FALSE
)Code
data_misfs_b |>
summarytools::descr(
var = mbepr_beipr,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)mbepr_beipr variable.
| mbepr_beipr | |
|---|---|
| Mean | 0.10 |
| Std.Dev | 0.06 |
| Min | 0.00 |
| Q1 | 0.06 |
| Median | 0.09 |
| Q3 | 0.12 |
| Max | 0.89 |
| MAD | 0.05 |
| IQR | 0.06 |
| CV | 0.61 |
| Skewness | 2.16 |
| SE.Skewness | 0.01 |
| Kurtosis | 10.79 |
| N.Valid | 31734.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data_misfs_b |>
plot_dist(
col = "mbepr_beipr",
jitter = FALSE
)Code
data_misfs_b |>
summarytools::descr(
var = maper,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)maper variable.
| maper | |
|---|---|
| Mean | 0.02 |
| Std.Dev | 0.02 |
| Min | 0.00 |
| Q1 | 0.01 |
| Median | 0.01 |
| Q3 | 0.03 |
| Max | 0.75 |
| MAD | 0.01 |
| IQR | 0.02 |
| CV | 1.22 |
| Skewness | 5.57 |
| SE.Skewness | 0.01 |
| Kurtosis | 78.88 |
| N.Valid | 31734.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data_misfs_b |>
plot_dist(
col = "maper",
jitter = FALSE
)Code
data_misfs_b |>
summarytools::descr(
var = mpepr,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)mpepr variable.
| mpepr | |
|---|---|
| Mean | 0.02 |
| Std.Dev | 0.02 |
| Min | 0.00 |
| Q1 | 0.01 |
| Median | 0.02 |
| Q3 | 0.03 |
| Max | 0.40 |
| MAD | 0.01 |
| IQR | 0.02 |
| CV | 0.81 |
| Skewness | 2.18 |
| SE.Skewness | 0.01 |
| Kurtosis | 13.89 |
| N.Valid | 31734.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data_misfs_b |>
plot_dist(
col = "mpepr",
jitter = FALSE
)Code
data_misfs_b |>
summarytools::descr(
var = maper_mpepr,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)maper_mpepr variable.
| maper_mpepr | |
|---|---|
| Mean | 0.04 |
| Std.Dev | 0.04 |
| Min | 0.00 |
| Q1 | 0.02 |
| Median | 0.04 |
| Q3 | 0.06 |
| Max | 0.75 |
| MAD | 0.02 |
| IQR | 0.03 |
| CV | 0.83 |
| Skewness | 3.18 |
| SE.Skewness | 0.01 |
| Kurtosis | 26.11 |
| N.Valid | 31734.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data_misfs_b |>
plot_dist(
col = "maper_mpepr",
jitter = FALSE
)Code
data_misfs_b |>
summarytools::descr(
var = gdp_per_capita,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)gdp_per_capita variable.
| gdp_per_capita | |
|---|---|
| Mean | 23457.49 |
| Std.Dev | 23488.35 |
| Min | 2729.65 |
| Q1 | 11984.65 |
| Median | 18584.56 |
| Q3 | 27952.20 |
| Max | 815697.80 |
| MAD | 11122.91 |
| IQR | 15967.55 |
| CV | 1.00 |
| Skewness | 9.28 |
| SE.Skewness | 0.01 |
| Kurtosis | 182.88 |
| N.Valid | 29045.00 |
| Pct.Valid | 91.53 |
Source: Created by the authors.
Code
data_misfs_b |>
plot_dist(
col = "gdp_per_capita",
jitter = FALSE
)Code
data_misfs_b |>
summarytools::descr(
var = spei_12m,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)spei_12m variable.
| spei_12m | |
|---|---|
| Mean | -0.08 |
| Std.Dev | 0.36 |
| Min | -1.24 |
| Q1 | -0.34 |
| Median | -0.07 |
| Q3 | 0.17 |
| Max | 0.78 |
| MAD | 0.37 |
| IQR | 0.51 |
| CV | -4.74 |
| Skewness | -0.01 |
| SE.Skewness | 0.01 |
| Kurtosis | -0.58 |
| N.Valid | 31734.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data_misfs_b |>
plot_dist(
col = "spei_12m",
jitter = FALSE
)C
Code
data_misfs_c |>
summarytools::freq(
var = year,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)year variable.
| Freq | % Valid | % Valid Cum. | % Total | % Total Cum. | |
|---|---|---|---|---|---|
| 2008 | 1625 | 8.00 | 8.00 | 8.00 | 8.00 |
| 2009 | 1702 | 8.37 | 16.37 | 8.37 | 16.37 |
| 2010 | 1690 | 8.32 | 24.69 | 8.32 | 24.69 |
| 2011 | 1700 | 8.36 | 33.05 | 8.36 | 33.05 |
| 2012 | 1728 | 8.50 | 41.55 | 8.50 | 41.55 |
| 2013 | 1685 | 8.29 | 49.84 | 8.29 | 49.84 |
| 2014 | 1700 | 8.36 | 58.21 | 8.36 | 58.21 |
| 2015 | 1705 | 8.39 | 66.60 | 8.39 | 66.60 |
| 2016 | 1718 | 8.45 | 75.05 | 8.45 | 75.05 |
| 2017 | 1704 | 8.38 | 83.43 | 8.38 | 83.43 |
| 2018 | 1668 | 8.21 | 91.64 | 8.21 | 91.64 |
| 2019 | 1699 | 8.36 | 100.00 | 8.36 | 100.00 |
| <NA> | 0 | 0.00 | 100.00 | ||
| Total | 20324 | 100.00 | 100.00 | 100.00 | 100.00 |
Source: Created by the authors.
Code
data_misfs_c |>
plot_bar(
col = "year",
y_label = "year"
)Code
data_misfs_c |>
summarytools::descr(
var = number_of_children,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)number_of_children variable.
| number_of_children | |
|---|---|
| Mean | 2439.41 |
| Std.Dev | 7494.04 |
| Min | 96.00 |
| Q1 | 636.00 |
| Median | 1213.00 |
| Q3 | 2206.00 |
| Max | 206458.00 |
| MAD | 1024.48 |
| IQR | 1570.00 |
| CV | 3.07 |
| Skewness | 16.77 |
| SE.Skewness | 0.02 |
| Kurtosis | 368.16 |
| N.Valid | 20324.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data_misfs_c |>
plot_dist(
col = "number_of_children",
jitter = FALSE
)Code
data_misfs_c |>
summarytools::descr(
var = sisvan_cover,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)sisvan_cover variable.
| sisvan_cover | |
|---|---|
| Mean | 0.50 |
| Std.Dev | 0.19 |
| Min | 0.05 |
| Q1 | 0.36 |
| Median | 0.49 |
| Q3 | 0.62 |
| Max | 1.00 |
| MAD | 0.20 |
| IQR | 0.27 |
| CV | 0.39 |
| Skewness | 0.17 |
| SE.Skewness | 0.02 |
| Kurtosis | -0.36 |
| N.Valid | 20324.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data_misfs_c |>
plot_dist(
col = "sisvan_cover",
jitter = FALSE
)Code
data_misfs_c |>
summarytools::descr(
var = mbepr,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)mbepr variable.
| mbepr | |
|---|---|
| Mean | 0.07 |
| Std.Dev | 0.04 |
| Min | 0.00 |
| Q1 | 0.04 |
| Median | 0.06 |
| Q3 | 0.08 |
| Max | 0.71 |
| MAD | 0.03 |
| IQR | 0.04 |
| CV | 0.64 |
| Skewness | 3.00 |
| SE.Skewness | 0.02 |
| Kurtosis | 20.44 |
| N.Valid | 20324.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data_misfs_c |>
plot_dist(
col = "mbepr",
jitter = FALSE
)Code
data_misfs_c |>
summarytools::descr(
var = beipr,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)beipr variable.
| beipr | |
|---|---|
| Mean | 0.08 |
| Std.Dev | 0.03 |
| Min | 0.00 |
| Q1 | 0.06 |
| Median | 0.07 |
| Q3 | 0.09 |
| Max | 0.38 |
| MAD | 0.03 |
| IQR | 0.03 |
| CV | 0.40 |
| Skewness | 1.12 |
| SE.Skewness | 0.02 |
| Kurtosis | 2.98 |
| N.Valid | 20324.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data_misfs_c |>
plot_dist(
col = "beipr",
jitter = FALSE
)Code
data_misfs_c |>
summarytools::descr(
var = mbepr_beipr,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)mbepr_beipr variable.
| mbepr_beipr | |
|---|---|
| Mean | 0.14 |
| Std.Dev | 0.07 |
| Min | 0.00 |
| Q1 | 0.10 |
| Median | 0.13 |
| Q3 | 0.17 |
| Max | 0.78 |
| MAD | 0.05 |
| IQR | 0.07 |
| CV | 0.45 |
| Skewness | 1.69 |
| SE.Skewness | 0.02 |
| Kurtosis | 6.25 |
| N.Valid | 20324.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data_misfs_c |>
plot_dist(
col = "mbepr_beipr",
jitter = FALSE
)Code
data_misfs_c |>
summarytools::descr(
var = maper,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)maper variable.
| maper | |
|---|---|
| Mean | 0.03 |
| Std.Dev | 0.03 |
| Min | 0.00 |
| Q1 | 0.02 |
| Median | 0.03 |
| Q3 | 0.04 |
| Max | 0.69 |
| MAD | 0.02 |
| IQR | 0.02 |
| CV | 0.85 |
| Skewness | 5.82 |
| SE.Skewness | 0.02 |
| Kurtosis | 73.54 |
| N.Valid | 20324.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data_misfs_c |>
plot_dist(
col = "maper",
jitter = FALSE
)Code
data_misfs_c |>
summarytools::descr(
var = mpepr,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)mpepr variable.
| mpepr | |
|---|---|
| Mean | 0.03 |
| Std.Dev | 0.02 |
| Min | 0.00 |
| Q1 | 0.02 |
| Median | 0.03 |
| Q3 | 0.04 |
| Max | 0.26 |
| MAD | 0.01 |
| IQR | 0.02 |
| CV | 0.48 |
| Skewness | 1.42 |
| SE.Skewness | 0.02 |
| Kurtosis | 6.23 |
| N.Valid | 20324.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data_misfs_c |>
plot_dist(
col = "mpepr",
jitter = FALSE
)Code
data_misfs_c |>
summarytools::descr(
var = maper_mpepr,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)maper_mpepr variable.
| maper_mpepr | |
|---|---|
| Mean | 0.07 |
| Std.Dev | 0.04 |
| Min | 0.00 |
| Q1 | 0.04 |
| Median | 0.06 |
| Q3 | 0.08 |
| Max | 0.74 |
| MAD | 0.03 |
| IQR | 0.04 |
| CV | 0.58 |
| Skewness | 3.47 |
| SE.Skewness | 0.02 |
| Kurtosis | 29.22 |
| N.Valid | 20324.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data_misfs_c |>
plot_dist(
col = "maper_mpepr",
jitter = FALSE
)Code
data_misfs_c |>
summarytools::descr(
var = gdp_per_capita,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)gdp_per_capita variable.
| gdp_per_capita | |
|---|---|
| Mean | 8964.53 |
| Std.Dev | 9688.17 |
| Min | 301.61 |
| Q1 | 5145.99 |
| Median | 6999.36 |
| Q3 | 9466.20 |
| Max | 296621.36 |
| MAD | 3086.89 |
| IQR | 4320.21 |
| CV | 1.08 |
| Skewness | 9.54 |
| SE.Skewness | 0.02 |
| Kurtosis | 162.45 |
| N.Valid | 18633.00 |
| Pct.Valid | 91.68 |
Source: Created by the authors.
Code
data_misfs_c |>
plot_dist(
col = "gdp_per_capita",
jitter = FALSE
)Code
data_misfs_c |>
summarytools::descr(
var = spei_12m,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)spei_12m variable.
| spei_12m | |
|---|---|
| Mean | -0.29 |
| Std.Dev | 0.45 |
| Min | -1.42 |
| Q1 | -0.63 |
| Median | -0.34 |
| Q3 | 0.05 |
| Max | 0.89 |
| MAD | 0.48 |
| IQR | 0.67 |
| CV | -1.57 |
| Skewness | 0.23 |
| SE.Skewness | 0.02 |
| Kurtosis | -0.61 |
| N.Valid | 20324.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data_misfs_c |>
plot_dist(
col = "spei_12m",
jitter = FALSE
)D
Code
data_misfs_d |>
summarytools::freq(
var = year,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)year variable.
| Freq | % Valid | % Valid Cum. | % Total | % Total Cum. | |
|---|---|---|---|---|---|
| 2008 | 217 | 7.83 | 7.83 | 7.83 | 7.83 |
| 2009 | 227 | 8.19 | 16.03 | 8.19 | 16.03 |
| 2010 | 232 | 8.38 | 24.40 | 8.38 | 24.40 |
| 2011 | 232 | 8.38 | 32.78 | 8.38 | 32.78 |
| 2012 | 232 | 8.38 | 41.16 | 8.38 | 41.16 |
| 2013 | 235 | 8.48 | 49.64 | 8.48 | 49.64 |
| 2014 | 234 | 8.45 | 58.09 | 8.45 | 58.09 |
| 2015 | 236 | 8.52 | 66.61 | 8.52 | 66.61 |
| 2016 | 234 | 8.45 | 75.05 | 8.45 | 75.05 |
| 2017 | 233 | 8.41 | 83.47 | 8.41 | 83.47 |
| 2018 | 230 | 8.30 | 91.77 | 8.30 | 91.77 |
| 2019 | 228 | 8.23 | 100.00 | 8.23 | 100.00 |
| <NA> | 0 | 0.00 | 100.00 | ||
| Total | 2770 | 100.00 | 100.00 | 100.00 | 100.00 |
Source: Created by the authors.
Code
data_misfs_d |>
plot_bar(
col = "year",
y_label = "year"
)Code
data_misfs_d |>
summarytools::descr(
var = number_of_children,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)number_of_children variable.
| number_of_children | |
|---|---|
| Mean | 5458.81 |
| Std.Dev | 13582.98 |
| Min | 274.00 |
| Q1 | 1730.00 |
| Median | 2901.50 |
| Q3 | 5084.00 |
| Max | 176505.00 |
| MAD | 2058.59 |
| IQR | 3353.50 |
| CV | 2.49 |
| Skewness | 9.79 |
| SE.Skewness | 0.05 |
| Kurtosis | 110.53 |
| N.Valid | 2770.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data_misfs_d |>
plot_dist(
col = "number_of_children",
jitter = FALSE
)Code
data_misfs_d |>
summarytools::descr(
var = sisvan_cover,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)sisvan_cover variable.
| sisvan_cover | |
|---|---|
| Mean | 0.37 |
| Std.Dev | 0.18 |
| Min | 0.05 |
| Q1 | 0.22 |
| Median | 0.34 |
| Q3 | 0.49 |
| Max | 1.00 |
| MAD | 0.20 |
| IQR | 0.27 |
| CV | 0.50 |
| Skewness | 0.59 |
| SE.Skewness | 0.05 |
| Kurtosis | 0.00 |
| N.Valid | 2770.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data_misfs_d |>
plot_dist(
col = "sisvan_cover",
jitter = FALSE
)Code
data_misfs_d |>
summarytools::descr(
var = mbepr,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)mbepr variable.
| mbepr | |
|---|---|
| Mean | 0.09 |
| Std.Dev | 0.06 |
| Min | 0.00 |
| Q1 | 0.06 |
| Median | 0.08 |
| Q3 | 0.11 |
| Max | 0.70 |
| MAD | 0.04 |
| IQR | 0.05 |
| CV | 0.60 |
| Skewness | 2.83 |
| SE.Skewness | 0.05 |
| Kurtosis | 15.78 |
| N.Valid | 2770.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data_misfs_d |>
plot_dist(
col = "mbepr",
jitter = FALSE
)Code
data_misfs_d |>
summarytools::descr(
var = beipr,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)beipr variable.
| beipr | |
|---|---|
| Mean | 0.13 |
| Std.Dev | 0.05 |
| Min | 0.00 |
| Q1 | 0.09 |
| Median | 0.12 |
| Q3 | 0.15 |
| Max | 0.37 |
| MAD | 0.04 |
| IQR | 0.06 |
| CV | 0.36 |
| Skewness | 0.82 |
| SE.Skewness | 0.05 |
| Kurtosis | 1.03 |
| N.Valid | 2770.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data_misfs_d |>
plot_dist(
col = "beipr",
jitter = FALSE
)Code
data_misfs_d |>
summarytools::descr(
var = mbepr_beipr,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)mbepr_beipr variable.
| mbepr_beipr | |
|---|---|
| Mean | 0.22 |
| Std.Dev | 0.09 |
| Min | 0.02 |
| Q1 | 0.16 |
| Median | 0.21 |
| Q3 | 0.27 |
| Max | 0.77 |
| MAD | 0.08 |
| IQR | 0.11 |
| CV | 0.40 |
| Skewness | 1.15 |
| SE.Skewness | 0.05 |
| Kurtosis | 2.43 |
| N.Valid | 2770.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data_misfs_d |>
plot_dist(
col = "mbepr_beipr",
jitter = FALSE
)Code
data_misfs_d |>
summarytools::descr(
var = maper,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)maper variable.
| maper | |
|---|---|
| Mean | 0.03 |
| Std.Dev | 0.02 |
| Min | 0.00 |
| Q1 | 0.02 |
| Median | 0.02 |
| Q3 | 0.03 |
| Max | 0.25 |
| MAD | 0.01 |
| IQR | 0.02 |
| CV | 0.70 |
| Skewness | 3.74 |
| SE.Skewness | 0.05 |
| Kurtosis | 26.00 |
| N.Valid | 2770.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data_misfs_d |>
plot_dist(
col = "maper",
jitter = FALSE
)Code
data_misfs_d |>
summarytools::descr(
var = mpepr,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)mpepr variable.
| mpepr | |
|---|---|
| Mean | 0.03 |
| Std.Dev | 0.02 |
| Min | 0.00 |
| Q1 | 0.02 |
| Median | 0.03 |
| Q3 | 0.04 |
| Max | 0.58 |
| MAD | 0.01 |
| IQR | 0.02 |
| CV | 0.54 |
| Skewness | 9.89 |
| SE.Skewness | 0.05 |
| Kurtosis | 256.68 |
| N.Valid | 2770.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data_misfs_d |>
plot_dist(
col = "mpepr",
jitter = FALSE
)Code
data_misfs_d |>
summarytools::descr(
var = maper_mpepr,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)maper_mpepr variable.
| maper_mpepr | |
|---|---|
| Mean | 0.06 |
| Std.Dev | 0.03 |
| Min | 0.00 |
| Q1 | 0.04 |
| Median | 0.06 |
| Q3 | 0.08 |
| Max | 0.59 |
| MAD | 0.02 |
| IQR | 0.03 |
| CV | 0.53 |
| Skewness | 3.61 |
| SE.Skewness | 0.05 |
| Kurtosis | 33.01 |
| N.Valid | 2770.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data_misfs_d |>
plot_dist(
col = "maper_mpepr",
jitter = FALSE
)Code
data_misfs_d |>
summarytools::descr(
var = gdp_per_capita,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)gdp_per_capita variable.
| gdp_per_capita | |
|---|---|
| Mean | 11283.13 |
| Std.Dev | 14661.64 |
| Min | 1755.69 |
| Q1 | 6088.96 |
| Median | 8357.51 |
| Q3 | 12467.00 |
| Max | 291965.37 |
| MAD | 4242.41 |
| IQR | 6375.31 |
| CV | 1.30 |
| Skewness | 11.12 |
| SE.Skewness | 0.05 |
| Kurtosis | 172.80 |
| N.Valid | 2538.00 |
| Pct.Valid | 91.62 |
Source: Created by the authors.
Code
data_misfs_d |>
plot_dist(
col = "gdp_per_capita",
jitter = FALSE
)Code
data_misfs_d |>
summarytools::descr(
var = spei_12m,
style = "rmarkdown",
plain.ascii = FALSE,
headings = FALSE
)spei_12m variable.
| spei_12m | |
|---|---|
| Mean | -0.24 |
| Std.Dev | 0.37 |
| Min | -1.75 |
| Q1 | -0.45 |
| Median | -0.21 |
| Q3 | 0.02 |
| Max | 0.69 |
| MAD | 0.34 |
| IQR | 0.47 |
| CV | -1.54 |
| Skewness | -0.51 |
| SE.Skewness | 0.05 |
| Kurtosis | 0.28 |
| N.Valid | 2770.00 |
| Pct.Valid | 100.00 |
Source: Created by the authors.
Code
data_misfs_d |>
plot_dist(
col = "spei_12m",
jitter = FALSE
)Checking Correlations
Code
Code
Code
Modeling the Data
By s(spei_12m) + s(gdp_per_capita) + s(year, bs = "re") (Continuous year)
Code
mbepr_gam_1 <- mgcv::gam(
mbepr ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = 're'),
data = dplyr::mutate(data, year = as.integer(as.character(year))),
family = mgcv::betar(link = "logit"),
method = "REML"
)mbepr_gam_1 |> summary()
#>
#> Family: Beta regression(20.157)
#> Link function: logit
#>
#> Formula:
#> mbepr ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = "re")
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.861140640 0.007939905 -360.3495 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 8.584178134271 8.951945 1024.44780 < 2.22e-16 ***
#> s(gdp_per_capita) 8.927964225397 8.998280 6041.29339 < 2.22e-16 ***
#> s(year) 0.000007753096 1.000000 0.00577 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0464 Deviance explained = 10.6%
#> -REML = -1.1166e+05 Scale est. = 1 n = 57487Code
mbepr_gam_1 |>
summarise_r2(
dplyr::mutate(data, year = as.integer(as.character(year))) |>
nrow()
) |>
md_named_tibble()mbepr_gam_1 model.
| Value | Interpretation | Rule | |
|---|---|---|---|
| R2 | 0.0464015016 | weak | cohen1988 |
| SE | 0.0016397405 | NA | NA |
| Lower CI | 0.0431876692 | weak | cohen1988 |
| Upper CI | 0.0496153339 | weak | cohen1988 |
Source: Created by the authors.
Code
mbepr_gam_1 |>
broom::glance() |>
tidyr::pivot_longer(dplyr::everything()) |>
md_named_tibble()mbepr_gam_1 model.
| Value | |
|---|---|
| df | 18.5121501128 |
| logLik | 111724.8198784178 |
| AIC | -223409.7392750263 |
| BIC | -223230.9988001064 |
| deviance | 59164.5555004290 |
| df.residual | 57468.4878498872 |
| nobs | 57487.0000000000 |
| adj.r.squared | 0.0464015016 |
| npar | 20.0000000000 |
Source: Created by the authors.
Code
mbepr_gam_1 |>
summarise_coefs() |>
md_named_tibble()mbepr_gam_1 model.
| Value | |
|---|---|
| [Mean] | -0.5258939556 |
| (Intercept) | -2.8611406401 |
| mean(s(spei_12m)) | -0.0490184501 |
| mean(s(gdp_per_capita)) | -0.8017302993 |
| mean(s(year)) | 0.0000002724 |
Source: Created by the authors.
Code
Code
mbepr_gam_1 |> mgcViz::getViz() |> mgcViz::check.gamViz()
#>
#> Method: REML Optimizer: outer newton
#> full convergence after 8 iterations.
#> Gradient range [0.00000000006809441899,0.002879607161]
#> (score -111661.2122 & scale 1).
#> eigenvalue range [-0.002879561729,24562.5239].
#> Model rank = 20 / 20
#>
#> Basis dimension (k) checking results. Low p-value (k-index<1) may
#> indicate that k is too low, especially if edf is close to k'.
#>
#> k' edf k-index p-value
#> s(spei_12m) 9.00000000 8.58417813 1.00 0.69
#> s(gdp_per_capita) 9.00000000 8.92796423 1.03 0.98
#> s(year) 1.00000000 0.00000775 1.00 0.70
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.Code
dplyr::mutate(data, year = as.integer(as.character(year))) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam(
model = mbepr_gam_1,
type = 1,
x_label = "Standardised Precipitation Evapotranspiration Index (12 months)",
y_label = "Predicted probability of MBEPR"
)mbepr_gam_1 model. All other variables are held constant at their mean values except SPEI. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
Code
beipr_gam_1 <- mgcv::gam(
beipr ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = 're'),
data = dplyr::mutate(data, year = as.integer(as.character(year))),
family = mgcv::betar(link = "logit"),
method = "REML"
)beipr_gam_1 |> summary()
#>
#> Family: Beta regression(28.99)
#> Link function: logit
#>
#> Formula:
#> beipr ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = "re")
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.674224178 0.005226234 -511.6924 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 8.425216648125 8.910154 854.90605 < 2.22e-16 ***
#> s(gdp_per_capita) 8.947331900629 8.999076 5886.02651 < 2.22e-16 ***
#> s(year) 0.000004093323 1.000000 0.00483 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0711 Deviance explained = 10%
#> -REML = -1.0699e+05 Scale est. = 1 n = 57487Code
beipr_gam_1 |>
summarise_r2(
dplyr::mutate(data, year = as.integer(as.character(year))) |>
nrow()
) |>
md_named_tibble()beipr_gam_1 model.
| Value | Interpretation | Rule | |
|---|---|---|---|
| R2 | 0.0711058142 | weak | cohen1988 |
| SE | 0.0019772535 | NA | NA |
| Lower CI | 0.0672304686 | weak | cohen1988 |
| Upper CI | 0.0749811599 | weak | cohen1988 |
Source: Created by the authors.
Code
beipr_gam_1 |>
broom::glance() |>
tidyr::pivot_longer(dplyr::everything()) |>
md_named_tibble()beipr_gam_1 model.
| Value | |
|---|---|
| df | 18.3725526421 |
| logLik | 107054.6958721782 |
| AIC | -214069.6633168273 |
| BIC | -213891.6935860782 |
| deviance | 58610.8595242622 |
| df.residual | 57468.6274473579 |
| nobs | 57487.0000000000 |
| adj.r.squared | 0.0711058142 |
| npar | 20.0000000000 |
Source: Created by the authors.
Code
beipr_gam_1 |>
summarise_coefs() |>
md_named_tibble()beipr_gam_1 model.
| Value | |
|---|---|
| [Mean] | -0.4755978616 |
| (Intercept) | -2.6742241784 |
| mean(s(spei_12m)) | -0.0967267012 |
| mean(s(gdp_per_capita)) | -0.6630214329 |
| mean(s(year)) | 0.0000001527 |
Source: Created by the authors.
Code
beipr_gam_1 |> mgcViz::getViz() |> mgcViz::check.gamViz()
#>
#> Method: REML Optimizer: outer newton
#> full convergence after 8 iterations.
#> Gradient range [-0.00000006091556815,0.002413588126]
#> (score -106990.7168 & scale 1).
#> eigenvalue range [-0.002413568672,26826.66028].
#> Model rank = 20 / 20
#>
#> Basis dimension (k) checking results. Low p-value (k-index<1) may
#> indicate that k is too low, especially if edf is close to k'.
#>
#> k' edf k-index p-value
#> s(spei_12m) 9.00000000 8.42521665 1.00 0.65
#> s(gdp_per_capita) 9.00000000 8.94733190 0.99 0.48
#> s(year) 1.00000000 0.00000409 0.99 0.53
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.Code
dplyr::mutate(data, year = as.integer(as.character(year))) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam(
model = beipr_gam_1,
type = 1,
x_label = "Standardised Precipitation Evapotranspiration Index (12 months)",
y_label = "Predicted probability of BEIPR"
)beipr_gam_1 model. All other variables are held constant at their mean values except SPEI. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
Code
mbepr_beipr_gam_1 <- mgcv::gam(
mbepr_beipr ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = 're'),
data = dplyr::mutate(data, year = as.integer(as.character(year))),
family = mgcv::betar(link = "logit"),
method = "REML"
)mbepr_beipr_gam_1 |> summary()
#>
#> Family: Beta regression(18.549)
#> Link function: logit
#>
#> Formula:
#> mbepr_beipr ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = "re")
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -1.991809900 0.008055182 -247.2706 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 8.21138174291 8.835775 500.6104 < 2.22e-16 ***
#> s(gdp_per_capita) 8.95132416042 8.999211 6612.0255 < 2.22e-16 ***
#> s(year) 0.00001281605 1.000000 0.0069 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0928 Deviance explained = 11%
#> -REML = -75501 Scale est. = 1 n = 57487Code
mbepr_beipr_gam_1 |>
summarise_r2(
dplyr::mutate(data, year = as.integer(as.character(year))) |>
nrow()
) |>
md_named_tibble()mbepr_beipr_gam_1 model.
| Value | Interpretation | Rule | |
|---|---|---|---|
| R2 | 0.0927744057 | weak | cohen1988 |
| SE | 0.0022058345 | NA | NA |
| Lower CI | 0.0884510494 | weak | cohen1988 |
| Upper CI | 0.0970977620 | weak | cohen1988 |
Source: Created by the authors.
Code
mbepr_beipr_gam_1 |>
broom::glance() |>
tidyr::pivot_longer(dplyr::everything()) |>
md_named_tibble()mbepr_beipr_gam_1 model.
| Value | |
|---|---|
| df | 18.1627187194 |
| logLik | 75564.1684419054 |
| AIC | -151088.7545047294 |
| BIC | -150911.4390209391 |
| deviance | 56826.7250717344 |
| df.residual | 57468.8372812806 |
| nobs | 57487.0000000000 |
| adj.r.squared | 0.0927744057 |
| npar | 20.0000000000 |
Source: Created by the authors.
Code
mbepr_beipr_gam_1 |>
summarise_coefs() |>
md_named_tibble()mbepr_beipr_gam_1 model.
| Value | |
|---|---|
| [Mean] | -0.4327391520 |
| (Intercept) | -1.9918098995 |
| mean(s(spei_12m)) | -0.0491642639 |
| mean(s(gdp_per_capita)) | -0.6911661198 |
| mean(s(year)) | 0.0000003130 |
Source: Created by the authors.
Code
Code
mbepr_beipr_gam_1 |> mgcViz::getViz() |> mgcViz::check.gamViz()
#>
#> Method: REML Optimizer: outer newton
#> full convergence after 7 iterations.
#> Gradient range [-0.000000000002437161584,0.003442248851]
#> (score -75501.36548 & scale 1).
#> eigenvalue range [-0.0034421609,28216.20368].
#> Model rank = 20 / 20
#>
#> Basis dimension (k) checking results. Low p-value (k-index<1) may
#> indicate that k is too low, especially if edf is close to k'.
#>
#> k' edf k-index p-value
#> s(spei_12m) 9.0000000 8.2113817 0.97 0.025 *
#> s(gdp_per_capita) 9.0000000 8.9513242 1.00 0.605
#> s(year) 1.0000000 0.0000128 0.98 0.100 .
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.Code
dplyr::mutate(data, year = as.integer(as.character(year))) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam(
model = mbepr_beipr_gam_1,
type = 1,
x_label = "Standardised Precipitation Evapotranspiration Index (12 months)",
y_label = "Predicted probability of MBEPR & BEIPR"
)mbepr_beipr_gam_1 model. All other variables are held constant at their mean values except SPEI. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
Code
maper_gam_1 <- mgcv::gam(
maper ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = 're'),
data = dplyr::mutate(data, year = as.integer(as.character(year))),
family = mgcv::betar(link = "logit"),
method = "REML"
)maper_gam_1 |> summary()
#>
#> Family: Beta regression(29.294)
#> Link function: logit
#>
#> Formula:
#> maper ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = "re")
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.736553835 0.005585534 -668.9699 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 8.713679695384 8.976808 1763.49787 < 2.22e-16 ***
#> s(gdp_per_capita) 8.924353007769 8.998108 7582.65249 < 2.22e-16 ***
#> s(year) 0.000002266183 1.000000 0.00119 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0322 Deviance explained = 13.5%
#> -REML = -1.6507e+05 Scale est. = 1 n = 57487Code
maper_gam_1 |>
summarise_r2(
dplyr::mutate(data, year = as.integer(as.character(year))) |>
nrow()
) |>
md_named_tibble()maper_gam_1 model.
| Value | Interpretation | Rule | |
|---|---|---|---|
| R2 | 0.0322449945 | weak | cohen1988 |
| SE | 0.0013872034 | NA | NA |
| Lower CI | 0.0295261259 | weak | cohen1988 |
| Upper CI | 0.0349638631 | weak | cohen1988 |
Source: Created by the authors.
Code
maper_gam_1 |>
broom::glance() |>
tidyr::pivot_longer(dplyr::everything()) |>
md_named_tibble()maper_gam_1 model.
| Value | |
|---|---|
| df | 18.6380349693 |
| logLik | 165139.1395496105 |
| AIC | -330238.3292586125 |
| BIC | -330059.3676731999 |
| deviance | 61134.5281416165 |
| df.residual | 57468.3619650307 |
| nobs | 57487.0000000000 |
| adj.r.squared | 0.0322449945 |
| npar | 20.0000000000 |
Source: Created by the authors.
Code
maper_gam_1 |>
summarise_coefs() |>
md_named_tibble()maper_gam_1 model.
| Value | |
|---|---|
| [Mean] | -0.6384154007 |
| (Intercept) | -3.7365538353 |
| mean(s(spei_12m)) | -0.0787088951 |
| mean(s(gdp_per_capita)) | -0.9248193552 |
| mean(s(year)) | 0.0000000731 |
Source: Created by the authors.
Code
maper_gam_1 |> mgcViz::getViz() |> mgcViz::check.gamViz()
#>
#> Method: REML Optimizer: outer newton
#> full convergence after 6 iterations.
#> Gradient range [-0.000004367680993,0.1862390108]
#> (score -165074.1951 & scale 1).
#> eigenvalue range [-0.0005940676576,20469.89394].
#> Model rank = 20 / 20
#>
#> Basis dimension (k) checking results. Low p-value (k-index<1) may
#> indicate that k is too low, especially if edf is close to k'.
#>
#> k' edf k-index p-value
#> s(spei_12m) 9.00000000 8.71367970 0.99 0.17
#> s(gdp_per_capita) 9.00000000 8.92435301 1.00 0.50
#> s(year) 1.00000000 0.00000227 0.98 0.11
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.Code
dplyr::mutate(data, year = as.integer(as.character(year))) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam(
model = maper_gam_1,
type = 1,
x_label = "Standardised Precipitation Evapotranspiration Index (12 months)",
y_label = "Predicted probability of MAPER"
)maper_gam_1 model. All other variables are held constant at their mean values except SPEI. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
Code
mpepr_gam_1 <- mgcv::gam(
mpepr ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = 're'),
data = dplyr::mutate(data, year = as.integer(as.character(year))),
family = mgcv::betar(link = "logit"),
method = "REML"
)mpepr_gam_1 |> summary()
#>
#> Family: Beta regression(36.492)
#> Link function: logit
#>
#> Formula:
#> mpepr ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = "re")
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.583160045 0.005421933 -660.864 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 8.745036118318 8.981492 2640.23084 < 2.22e-16 ***
#> s(gdp_per_capita) 8.931163034062 8.998426 7336.39793 < 2.22e-16 ***
#> s(year) 0.000002694927 1.000000 0.00239 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0261 Deviance explained = 14%
#> -REML = -1.5199e+05 Scale est. = 1 n = 57487Code
mpepr_gam_1 |>
summarise_r2(
dplyr::mutate(data, year = as.integer(as.character(year))) |>
nrow()
) |>
md_named_tibble()mpepr_gam_1 model.
| Value | Interpretation | Rule | |
|---|---|---|---|
| R2 | 0.0260845253 | weak | cohen1988 |
| SE | 0.0012556144 | NA | NA |
| Lower CI | 0.0236235663 | weak | cohen1988 |
| Upper CI | 0.0285454843 | weak | cohen1988 |
Source: Created by the authors.
Code
mpepr_gam_1 |>
broom::glance() |>
tidyr::pivot_longer(dplyr::everything()) |>
md_named_tibble()mpepr_gam_1 model.
| Value | |
|---|---|
| df | 18.6762018473 |
| logLik | 152056.3826799541 |
| AIC | -304072.8055124315 |
| BIC | -303893.7990996807 |
| deviance | 61556.6647899098 |
| df.residual | 57468.3237981527 |
| nobs | 57487.0000000000 |
| adj.r.squared | 0.0260845253 |
| npar | 20.0000000000 |
Source: Created by the authors.
Code
mpepr_gam_1 |>
summarise_coefs() |>
md_named_tibble()mpepr_gam_1 model.
| Value | |
|---|---|
| [Mean] | -0.5808609872 |
| (Intercept) | -3.5831600449 |
| mean(s(spei_12m)) | -0.0478663971 |
| mean(s(gdp_per_capita)) | -0.8448069142 |
| mean(s(year)) | 0.0000001039 |
Source: Created by the authors.
Code
mpepr_gam_1 |> mgcViz::getViz() |> mgcViz::check.gamViz()
#>
#> Method: REML Optimizer: outer newton
#> full convergence after 6 iterations.
#> Gradient range [-0.000002371916537,0.06498952371]
#> (score -151990.3073 & scale 1).
#> eigenvalue range [-0.001191916298,23090.53243].
#> Model rank = 20 / 20
#>
#> Basis dimension (k) checking results. Low p-value (k-index<1) may
#> indicate that k is too low, especially if edf is close to k'.
#>
#> k' edf k-index p-value
#> s(spei_12m) 9.00000000 8.74503612 0.99 0.42
#> s(gdp_per_capita) 9.00000000 8.93116303 0.99 0.27
#> s(year) 1.00000000 0.00000269 0.98 0.10
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.Code
dplyr::mutate(data, year = as.integer(as.character(year))) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam(
model = mpepr_gam_1,
type = 1,
x_label = "Standardised Precipitation Evapotranspiration Index (12 months)",
y_label = "Predicted probability of MPEPR"
)mpepr_gam_1 model. All other variables are held constant at their mean values except SPEI. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
Code
maper_mpepr_gam_1 <- mgcv::gam(
maper_mpepr ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = 're'),
data = dplyr::mutate(data, year = as.integer(as.character(year))),
family = mgcv::betar(link = "logit"),
method = "REML"
)maper_mpepr_gam_1 |> summary()
#>
#> Family: Beta regression(24.441)
#> Link function: logit
#>
#> Formula:
#> maper_mpepr ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = "re")
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.927179429 0.005399655 -542.1049 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 8.767998714279 8.984645 1966.20975 < 2.22e-16 ***
#> s(gdp_per_capita) 8.927338038815 8.998253 8023.77308 < 2.22e-16 ***
#> s(year) 0.000003094706 1.000000 0.00133 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0597 Deviance explained = 14.6%
#> -REML = -1.1628e+05 Scale est. = 1 n = 57487Code
maper_mpepr_gam_1 |>
summarise_r2(
dplyr::mutate(data, year = as.integer(as.character(year))) |>
nrow()
) |>
md_named_tibble()maper_mpepr_gam_1 model.
| Value | Interpretation | Rule | |
|---|---|---|---|
| R2 | 0.0596743943 | weak | cohen1988 |
| SE | 0.0018336474 | NA | NA |
| Lower CI | 0.0560805115 | weak | cohen1988 |
| Upper CI | 0.0632682771 | weak | cohen1988 |
Source: Created by the authors.
Code
maper_mpepr_gam_1 |>
broom::glance() |>
tidyr::pivot_longer(dplyr::everything()) |>
md_named_tibble()maper_mpepr_gam_1 model.
| Value | |
|---|---|
| df | 18.6953398478 |
| logLik | 116347.2518000684 |
| AIC | -232654.5377929083 |
| BIC | -232475.5046825131 |
| deviance | 59538.9739075563 |
| df.residual | 57468.3046601522 |
| nobs | 57487.0000000000 |
| adj.r.squared | 0.0596743943 |
| npar | 20.0000000000 |
Source: Created by the authors.
Code
maper_mpepr_gam_1 |>
summarise_coefs() |>
md_named_tibble()maper_mpepr_gam_1 model.
| Value | |
|---|---|
| [Mean] | -0.5164756841 |
| (Intercept) | -2.9271794294 |
| mean(s(spei_12m)) | -0.0129632359 |
| mean(s(gdp_per_capita)) | -0.8095183564 |
| mean(s(year)) | 0.0000000792 |
Source: Created by the authors.
Code
Code
maper_mpepr_gam_1 |> mgcViz::getViz() |> mgcViz::check.gamViz()
#>
#> Method: REML Optimizer: outer newton
#> full convergence after 6 iterations.
#> Gradient range [-0.0000000180332842,0.0006629463672]
#> (score -116280.8774 & scale 1).
#> eigenvalue range [-0.0006629420942,25021.01371].
#> Model rank = 20 / 20
#>
#> Basis dimension (k) checking results. Low p-value (k-index<1) may
#> indicate that k is too low, especially if edf is close to k'.
#>
#> k' edf k-index p-value
#> s(spei_12m) 9.00000000 8.76799871 1.00 0.750
#> s(gdp_per_capita) 9.00000000 8.92733804 0.99 0.430
#> s(year) 1.00000000 0.00000309 0.97 0.075 .
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.Code
dplyr::mutate(data, year = as.integer(as.character(year))) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam(
model = maper_mpepr_gam_1,
type = 1,
x_label = "Standardised Precipitation Evapotranspiration Index (12 months)",
y_label = "Predicted probability of MAPER & MPEPR"
)maper_mpepr_gam_1 model. All other variables are held constant at their mean values except SPEI. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
By s(spei_12m) + s(gdp_per_capita) + year (Ordered year)
In this model, the year variable is treated as a ordered categorical variable.
.L, .Q, and .C are, respectively, the coefficients for the ordered factor coded with linear, quadratic, and cubic contrasts.
mbepr_gam_2 |> summary()
#>
#> Family: Beta regression(20.626)
#> Link function: logit
#>
#> Formula:
#> mbepr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.867236822 0.003281149 -873.85133 < 2.22e-16 ***
#> year.L 0.334852405 0.015304979 21.87866 < 2.22e-16 ***
#> year.Q -0.190191728 0.011293836 -16.84031 < 2.22e-16 ***
#> year.C 0.029166943 0.011042189 2.64141 0.00825618 **
#> year^4 -0.034744005 0.010994303 -3.16018 0.00157670 **
#> year^5 0.065036783 0.011586423 5.61319 1.9863e-08 ***
#> year^6 -0.090152964 0.011470716 -7.85940 3.8597e-15 ***
#> year^7 0.037891711 0.011064506 3.42462 0.00061566 ***
#> year^8 0.083305795 0.011312349 7.36415 1.7828e-13 ***
#> year^9 -0.101055623 0.011498195 -8.78882 < 2.22e-16 ***
#> year^10 -0.005261888 0.010895385 -0.48295 0.62913371
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 8.590172 8.953754 260.0321 < 2.22e-16 ***
#> s(gdp_per_capita) 8.948270 8.999109 6695.3422 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0361 Deviance explained = 12.6%
#> -REML = -1.1223e+05 Scale est. = 1 n = 57487Code
mbepr_gam_2 |>
summarise_r2(
data |>
nrow()
) |>
md_named_tibble()mbepr_gam_2 model.
| Value | Interpretation | Rule | |
|---|---|---|---|
| R2 | 0.0361097497 | weak | cohen1988 |
| SE | 0.0014621212 | NA | NA |
| Lower CI | 0.0332440448 | weak | cohen1988 |
| Upper CI | 0.0389754546 | weak | cohen1988 |
Source: Created by the authors.
Code
mbepr_gam_2 |>
broom::glance() |>
tidyr::pivot_longer(dplyr::everything()) |>
md_named_tibble()mbepr_gam_2 model.
| Value | |
|---|---|
| df | 28.5384421900 |
| logLik | 112328.7929502070 |
| AIC | -224597.6801733562 |
| BIC | -224329.3230603794 |
| deviance | 59160.0001780340 |
| df.residual | 57458.4615578100 |
| nobs | 57487.0000000000 |
| adj.r.squared | 0.0361097497 |
| npar | 29.0000000000 |
Source: Created by the authors.
Code
mbepr_gam_2 |>
summarise_coefs() |>
md_named_tibble()mbepr_gam_2 model.
| Value | |
|---|---|
| [Mean] | -0.3903238155 |
| (Intercept) | -2.8672368221 |
| year.L | 0.3348524054 |
| year.Q | -0.1901917275 |
| year.C | 0.0291669434 |
| year^4 | -0.0347440046 |
| year^5 | 0.0650367833 |
| year^6 | -0.0901529636 |
| year^7 | 0.0378917115 |
| year^8 | 0.0833057953 |
| year^9 | -0.1010556227 |
| year^10 | -0.0052618883 |
| mean(s(spei_12m)) | -0.0268823140 |
| mean(s(gdp_per_capita)) | -0.9265622705 |
Source: Created by the authors.
Code
mbepr_gam_2 |> mgcViz::getViz() |> mgcViz::check.gamViz()
#>
#> Method: REML Optimizer: outer newton
#> full convergence after 6 iterations.
#> Gradient range [-0.000000007553492054,0.0001310561186]
#> (score -112228.2713 & scale 1).
#> Hessian positive definite, eigenvalue range [2.742501638,24607.56655].
#> Model rank = 29 / 29
#>
#> Basis dimension (k) checking results. Low p-value (k-index<1) may
#> indicate that k is too low, especially if edf is close to k'.
#>
#> k' edf k-index p-value
#> s(spei_12m) 9.00 8.59 0.98 0.10
#> s(gdp_per_capita) 9.00 8.95 0.99 0.27
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.Code
data |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam(
model = mbepr_gam_2,
type = 2,
x_label = "Standardised Precipitation Evapotranspiration Index (12 months)",
y_label = "Predicted probability of MBEPR"
)mbepr_gam_2 model. All other variables are held constant at their mean values except SPEI. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
beipr_gam_2 |> summary()
#>
#> Family: Beta regression(29.757)
#> Link function: logit
#>
#> Formula:
#> beipr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.679556058 0.002762283 -970.05121 < 2.22e-16 ***
#> year.L 0.379363757 0.012844958 29.53406 < 2.22e-16 ***
#> year.Q -0.073493595 0.009454281 -7.77358 7.6299e-15 ***
#> year.C -0.017737994 0.009260560 -1.91543 0.0554371 .
#> year^4 -0.018744860 0.009205861 -2.03619 0.0417315 *
#> year^5 0.040090504 0.009720607 4.12428 3.7190e-05 ***
#> year^6 -0.088111561 0.009657780 -9.12338 < 2.22e-16 ***
#> year^7 0.005715029 0.009274683 0.61620 0.5377647
#> year^8 0.063706394 0.009575102 6.65334 2.8652e-11 ***
#> year^9 -0.031224094 0.009720235 -3.21228 0.0013169 **
#> year^10 0.053974600 0.009221093 5.85338 4.8167e-09 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 8.087818 8.785738 129.7223 < 2.22e-16 ***
#> s(gdp_per_capita) 8.963470 8.999553 6882.1263 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0631 Deviance explained = 12.3%
#> -REML = -1.0766e+05 Scale est. = 1 n = 57487Code
beipr_gam_2 |>
summarise_r2(
data |>
nrow()
) |>
md_named_tibble()beipr_gam_2 model.
| Value | Interpretation | Rule | |
|---|---|---|---|
| R2 | 0.0631125811 | weak | cohen1988 |
| SE | 0.0018788362 | NA | NA |
| Lower CI | 0.0594301298 | weak | cohen1988 |
| Upper CI | 0.0667950325 | weak | cohen1988 |
Source: Created by the authors.
Code
beipr_gam_2 |>
broom::glance() |>
tidyr::pivot_longer(dplyr::everything()) |>
md_named_tibble()beipr_gam_2 model.
| Value | |
|---|---|
| df | 28.0512885520 |
| logLik | 107759.0063622705 |
| AIC | -215458.5539124896 |
| BIC | -215192.1988254745 |
| deviance | 58635.8529103905 |
| df.residual | 57458.9487114480 |
| nobs | 57487.0000000000 |
| adj.r.squared | 0.0631125811 |
| npar | 29.0000000000 |
Source: Created by the authors.
Code
beipr_gam_2 |>
summarise_coefs() |>
md_named_tibble()beipr_gam_2 model.
| Value | |
|---|---|
| [Mean] | -0.3476178903 |
| (Intercept) | -2.6795560580 |
| year.L | 0.3793637569 |
| year.Q | -0.0734935948 |
| year.C | -0.0177379944 |
| year^4 | -0.0187448596 |
| year^5 | 0.0400905045 |
| year^6 | -0.0881115613 |
| year^7 | 0.0057150295 |
| year^8 | 0.0637063939 |
| year^9 | -0.0312240945 |
| year^10 | 0.0539745997 |
| mean(s(spei_12m)) | -0.0761424849 |
| mean(s(gdp_per_capita)) | -0.7810687308 |
Source: Created by the authors.
Code
beipr_gam_2 |> mgcViz::getViz() |> mgcViz::check.gamViz()
#>
#> Method: REML Optimizer: outer newton
#> full convergence after 5 iterations.
#> Gradient range [0.00000007628327259,0.0008694519884]
#> (score -107658.5489 & scale 1).
#> Hessian positive definite, eigenvalue range [2.587987234,26850.58834].
#> Model rank = 29 / 29
#>
#> Basis dimension (k) checking results. Low p-value (k-index<1) may
#> indicate that k is too low, especially if edf is close to k'.
#>
#> k' edf k-index p-value
#> s(spei_12m) 9.00 8.09 0.99 0.34
#> s(gdp_per_capita) 9.00 8.96 0.97 0.12
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.Code
data |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam(
model = beipr_gam_2,
type = 2,
x_label = "Standardised Precipitation Evapotranspiration Index (12 months)",
y_label = "Predicted probability of BEIPR"
)beipr_gam_2 model. All other variables are held constant at their mean values except SPEI. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
mbepr_beipr_gam_2 |> summary()
#>
#> Family: Beta regression(18.821)
#> Link function: logit
#>
#> Formula:
#> mbepr_beipr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -1.993982846 0.002685691 -742.44691 < 2.22e-16 ***
#> year.L 0.232091903 0.012477038 18.60152 < 2.22e-16 ***
#> year.Q -0.081556995 0.009207992 -8.85720 < 2.22e-16 ***
#> year.C 0.006303070 0.009022933 0.69856 0.4848264
#> year^4 -0.017902893 0.008971719 -1.99548 0.0459905 *
#> year^5 0.053929139 0.009480922 5.68817 0.0000000128404427 ***
#> year^6 -0.092038681 0.009401276 -9.79002 < 2.22e-16 ***
#> year^7 0.028252073 0.009056075 3.11968 0.0018105 **
#> year^8 0.064366668 0.009298415 6.92233 0.0000000000044429 ***
#> year^9 -0.050756320 0.009473928 -5.35747 0.0000000843935688 ***
#> year^10 0.013876154 0.008985835 1.54423 0.1225338
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 7.619617 8.538673 121.8412 < 2.22e-16 ***
#> s(gdp_per_capita) 8.962548 8.999531 6728.9094 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0903 Deviance explained = 12.2%
#> -REML = -75868 Scale est. = 1 n = 57487Code
mbepr_beipr_gam_2 |>
summarise_r2(
data |>
nrow()
) |>
md_named_tibble()mbepr_beipr_gam_2 model.
| Value | Interpretation | Rule | |
|---|---|---|---|
| R2 | 0.0902584119 | weak | cohen1988 |
| SE | 0.0021817523 | NA | NA |
| Lower CI | 0.0859822559 | weak | cohen1988 |
| Upper CI | 0.0945345678 | weak | cohen1988 |
Source: Created by the authors.
Code
mbepr_beipr_gam_2 |>
broom::glance() |>
tidyr::pivot_longer(dplyr::everything()) |>
md_named_tibble()mbepr_beipr_gam_2 model.
| Value | |
|---|---|
| df | 27.5821646294 |
| logLik | 75966.5942130830 |
| AIC | -151874.1120177856 |
| BIC | -151609.4699680741 |
| deviance | 56843.8939035914 |
| df.residual | 57459.4178353706 |
| nobs | 57487.0000000000 |
| adj.r.squared | 0.0902584119 |
| npar | 29.0000000000 |
Source: Created by the authors.
Code
mbepr_beipr_gam_2 |>
summarise_coefs() |>
md_named_tibble()mbepr_beipr_gam_2 model.
| Value | |
|---|---|
| [Mean] | -0.3148429005 |
| (Intercept) | -1.9939828463 |
| year.L | 0.2320919026 |
| year.Q | -0.0815569951 |
| year.C | 0.0063030698 |
| year^4 | -0.0179028932 |
| year^5 | 0.0539291385 |
| year^6 | -0.0920386810 |
| year^7 | 0.0282520728 |
| year^8 | 0.0643666680 |
| year^9 | -0.0507563198 |
| year^10 | 0.0138761538 |
| mean(s(spei_12m)) | -0.0366551981 |
| mean(s(gdp_per_capita)) | -0.7736809556 |
Source: Created by the authors.
Code
Code
mbepr_beipr_gam_2 |> mgcViz::getViz() |> mgcViz::check.gamViz()
#>
#> Method: REML Optimizer: outer newton
#> full convergence after 8 iterations.
#> Gradient range [-0.0001292059854,0.0003324223279]
#> (score -75868.16565 & scale 1).
#> Hessian positive definite, eigenvalue range [1.430426406,28213.15345].
#> Model rank = 29 / 29
#>
#> Basis dimension (k) checking results. Low p-value (k-index<1) may
#> indicate that k is too low, especially if edf is close to k'.
#>
#> k' edf k-index p-value
#> s(spei_12m) 9.00 7.62 0.98 0.27
#> s(gdp_per_capita) 9.00 8.96 1.00 0.66
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.Code
data |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam(
model = mbepr_beipr_gam_2,
type = 2,
x_label = "Standardised Precipitation Evapotranspiration Index (12 months)",
y_label = "Predicted probability of MBEPR & BEIPR"
)mbepr_beipr_gam_2 model. All other variables are held constant at their mean values except SPEI. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
maper_gam_2 |> summary()
#>
#> Family: Beta regression(30.068)
#> Link function: logit
#>
#> Formula:
#> maper ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.745811394 0.003590307 -1043.31227 < 2.22e-16 ***
#> year.L 0.284451962 0.016747863 16.98437 < 2.22e-16 ***
#> year.Q -0.252746696 0.012370422 -20.43153 < 2.22e-16 ***
#> year.C -0.041954809 0.012055881 -3.48003 0.00050136 ***
#> year^4 -0.041283859 0.012062966 -3.42236 0.00062079 ***
#> year^5 0.078841216 0.012725742 6.19541 0.000000000581327 ***
#> year^6 -0.047537107 0.012600461 -3.77265 0.00016152 ***
#> year^7 0.079219649 0.012084358 6.55555 0.000000000055436 ***
#> year^8 0.152385939 0.012355872 12.33308 < 2.22e-16 ***
#> year^9 -0.126937979 0.012528186 -10.13219 < 2.22e-16 ***
#> year^10 0.066201041 0.011916908 5.55522 0.000000027726284 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 8.694710 8.973967 664.9771 < 2.22e-16 ***
#> s(gdp_per_capita) 8.944671 8.998983 7907.9297 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0196 Deviance explained = 15.5%
#> -REML = -1.6567e+05 Scale est. = 1 n = 57487Code
maper_gam_2 |>
summarise_r2(
data |>
nrow()
) |>
md_named_tibble()maper_gam_2 model.
| Value | Interpretation | Rule | |
|---|---|---|---|
| R2 | 0.0195525479 | very weak (negligible) | cohen1988 |
| SE | 0.0010943835 | NA | NA |
| Lower CI | 0.0174075956 | very weak (negligible) | cohen1988 |
| Upper CI | 0.0216975002 | weak | cohen1988 |
Source: Created by the authors.
Code
maper_gam_2 |>
broom::glance() |>
tidyr::pivot_longer(dplyr::everything()) |>
md_named_tibble()maper_gam_2 model.
| Value | |
|---|---|
| df | 28.6393814172 |
| logLik | 165771.6188545156 |
| AIC | -331483.2918093859 |
| BIC | -331214.7547369934 |
| deviance | 61106.8873587711 |
| df.residual | 57458.3606185828 |
| nobs | 57487.0000000000 |
| adj.r.squared | 0.0195525479 |
| npar | 29.0000000000 |
Source: Created by the authors.
Code
maper_gam_2 |>
summarise_coefs() |>
md_named_tibble()maper_gam_2 model.
| Value | |
|---|---|
| [Mean] | -0.4669379494 |
| (Intercept) | -3.7458113944 |
| year.L | 0.2844519617 |
| year.Q | -0.2527466962 |
| year.C | -0.0419548095 |
| year^4 | -0.0412838591 |
| year^5 | 0.0788412155 |
| year^6 | -0.0475371072 |
| year^7 | 0.0792196494 |
| year^8 | 0.1523859391 |
| year^9 | -0.1269379792 |
| year^10 | 0.0662010413 |
| mean(s(spei_12m)) | -0.0515535149 |
| mean(s(gdp_per_capita)) | -1.0535607621 |
Source: Created by the authors.
Code
maper_gam_2 |> mgcViz::getViz() |> mgcViz::check.gamViz()
#>
#> Method: REML Optimizer: outer newton
#> full convergence after 6 iterations.
#> Gradient range [-0.000002867504815,0.1272252185]
#> (score -165671.0735 & scale 1).
#> Hessian positive definite, eigenvalue range [3.108890111,20555.5479].
#> Model rank = 29 / 29
#>
#> Basis dimension (k) checking results. Low p-value (k-index<1) may
#> indicate that k is too low, especially if edf is close to k'.
#>
#> k' edf k-index p-value
#> s(spei_12m) 9.00 8.69 1 0.45
#> s(gdp_per_capita) 9.00 8.94 1 0.56
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.Code
data |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam(
model = maper_gam_2,
type = 2,
x_label = "Standardised Precipitation Evapotranspiration Index (12 months)",
y_label = "Predicted probability of MAPER"
)maper_gam_2 model. All other variables are held constant at their mean values except SPEI. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
mpepr_gam_2 |> summary()
#>
#> Family: Beta regression(37.457)
#> Link function: logit
#>
#> Formula:
#> mpepr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.591069631 0.003307189 -1085.83751 < 2.22e-16 ***
#> year.L 0.367855057 0.015442503 23.82095 < 2.22e-16 ***
#> year.Q -0.159533870 0.011391553 -14.00458 < 2.22e-16 ***
#> year.C -0.037310268 0.011039591 -3.37968 0.00072571 ***
#> year^4 -0.112980560 0.011066570 -10.20918 < 2.22e-16 ***
#> year^5 0.039551972 0.011649005 3.39531 0.00068551 ***
#> year^6 -0.017942377 0.011542848 -1.55442 0.12008545
#> year^7 0.035718527 0.011057339 3.23030 0.00123660 **
#> year^8 0.118922709 0.011338117 10.48875 < 2.22e-16 ***
#> year^9 -0.079238108 0.011493850 -6.89396 0.00000000000542614 ***
#> year^10 0.079527906 0.011014548 7.22026 0.00000000000051888 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 8.647503 8.965450 822.0245 < 2.22e-16 ***
#> s(gdp_per_capita) 8.951176 8.999205 7986.3431 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.00384 Deviance explained = 16.1%
#> -REML = -1.5263e+05 Scale est. = 1 n = 57487Code
mpepr_gam_2 |>
summarise_r2(
data |>
nrow()
) |>
md_named_tibble()mpepr_gam_2 model.
| Value | Interpretation | Rule | |
|---|---|---|---|
| R2 | 0.0038386871 | very weak (negligible) | cohen1988 |
| SE | 0.0004926796 | NA | NA |
| Lower CI | 0.0028730528 | very weak (negligible) | cohen1988 |
| Upper CI | 0.0048043214 | very weak (negligible) | cohen1988 |
Source: Created by the authors.
Code
mpepr_gam_2 |>
broom::glance() |>
tidyr::pivot_longer(dplyr::everything()) |>
md_named_tibble()mpepr_gam_2 model.
| Value | |
|---|---|
| df | 28.5986793746 |
| logLik | 152726.7044215834 |
| AIC | -305393.4795328694 |
| BIC | -305125.0167750669 |
| deviance | 61538.8824296959 |
| df.residual | 57458.4013206254 |
| nobs | 57487.0000000000 |
| adj.r.squared | 0.0038386871 |
| npar | 29.0000000000 |
Source: Created by the authors.
Code
mpepr_gam_2 |>
summarise_coefs() |>
md_named_tibble()mpepr_gam_2 model.
| Value | |
|---|---|
| [Mean] | -0.4291351369 |
| (Intercept) | -3.5910696309 |
| year.L | 0.3678550569 |
| year.Q | -0.1595338697 |
| year.C | -0.0373102681 |
| year^4 | -0.1129805604 |
| year^5 | 0.0395519722 |
| year^6 | -0.0179423769 |
| year^7 | 0.0357185269 |
| year^8 | 0.1189227087 |
| year^9 | -0.0792381076 |
| year^10 | 0.0795279064 |
| mean(s(spei_12m)) | -0.0288333047 |
| mean(s(gdp_per_capita)) | -0.9809911760 |
Source: Created by the authors.
Code
mpepr_gam_2 |> mgcViz::getViz() |> mgcViz::check.gamViz()
#>
#> Method: REML Optimizer: outer newton
#> full convergence after 5 iterations.
#> Gradient range [-0.00001519267452,0.03105131545]
#> (score -152625.1651 & scale 1).
#> Hessian positive definite, eigenvalue range [2.990365667,23167.47384].
#> Model rank = 29 / 29
#>
#> Basis dimension (k) checking results. Low p-value (k-index<1) may
#> indicate that k is too low, especially if edf is close to k'.
#>
#> k' edf k-index p-value
#> s(spei_12m) 9.00 8.65 0.98 0.09 .
#> s(gdp_per_capita) 9.00 8.95 1.01 0.82
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.Code
data |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam(
model = mpepr_gam_2,
type = 2,
x_label = "Standardised Precipitation Evapotranspiration Index (12 months)",
y_label = "Predicted probability of MPEPR"
)mpepr_gam_2 model. All other variables are held constant at their mean values except SPEI. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
maper_mpepr_gam_2 |> summary()
#>
#> Family: Beta regression(24.906)
#> Link function: logit
#>
#> Formula:
#> maper_mpepr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.932009662 0.003154015 -929.61194 < 2.22e-16 ***
#> year.L 0.225931702 0.014735767 15.33220 < 2.22e-16 ***
#> year.Q -0.170620538 0.010860320 -15.71045 < 2.22e-16 ***
#> year.C -0.045362482 0.010532400 -4.30695 1.6552e-05 ***
#> year^4 -0.086231457 0.010553933 -8.17055 3.0698e-16 ***
#> year^5 0.061553065 0.011116860 5.53691 3.0785e-08 ***
#> year^6 -0.015874857 0.011008964 -1.44199 0.1493
#> year^7 0.077181524 0.010556785 7.31108 2.6500e-13 ***
#> year^8 0.119533798 0.010806315 11.06148 < 2.22e-16 ***
#> year^9 -0.079353515 0.010970747 -7.23319 4.7177e-13 ***
#> year^10 0.057858181 0.010478759 5.52147 3.3617e-08 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 8.739492 8.980914 782.5095 < 2.22e-16 ***
#> s(gdp_per_capita) 8.945937 8.999029 7854.0728 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0487 Deviance explained = 16.1%
#> -REML = -1.1674e+05 Scale est. = 1 n = 57487Code
maper_mpepr_gam_2 |>
summarise_r2(
data |>
nrow()
) |>
md_named_tibble()maper_mpepr_gam_2 model.
| Value | Interpretation | Rule | |
|---|---|---|---|
| R2 | 0.0487055780 | weak | cohen1988 |
| SE | 0.0016758990 | NA | NA |
| Lower CI | 0.0454208762 | weak | cohen1988 |
| Upper CI | 0.0519902797 | weak | cohen1988 |
Source: Created by the authors.
Code
maper_mpepr_gam_2 |>
broom::glance() |>
tidyr::pivot_longer(dplyr::everything()) |>
md_named_tibble()maper_mpepr_gam_2 model.
| Value | |
|---|---|
| df | 28.685429756 |
| logLik | 116845.724333434 |
| AIC | -233631.488781632 |
| BIC | -233362.889058592 |
| deviance | 59536.185150791 |
| df.residual | 57458.314570244 |
| nobs | 57487.000000000 |
| adj.r.squared | 0.048705578 |
| npar | 29.000000000 |
Source: Created by the authors.
Code
maper_mpepr_gam_2 |>
summarise_coefs() |>
md_named_tibble()maper_mpepr_gam_2 model.
| Value | |
|---|---|
| [Mean] | -0.3774149887 |
| (Intercept) | -2.9320096620 |
| year.L | 0.2259317019 |
| year.Q | -0.1706205382 |
| year.C | -0.0453624821 |
| year^4 | -0.0862314575 |
| year^5 | 0.0615530651 |
| year^6 | -0.0158748575 |
| year^7 | 0.0771815244 |
| year^8 | 0.1195337978 |
| year^9 | -0.0793535149 |
| year^10 | 0.0578581812 |
| mean(s(spei_12m)) | 0.0017632820 |
| mean(s(gdp_per_capita)) | -0.9081677744 |
Source: Created by the authors.
Code
Code
maper_mpepr_gam_2 |> mgcViz::getViz() |> mgcViz::check.gamViz()
#>
#> Method: REML Optimizer: outer newton
#> full convergence after 5 iterations.
#> Gradient range [0.000000006063582525,0.0004676518962]
#> (score -116742.6877 & scale 1).
#> Hessian positive definite, eigenvalue range [3.173550905,25060.67586].
#> Model rank = 29 / 29
#>
#> Basis dimension (k) checking results. Low p-value (k-index<1) may
#> indicate that k is too low, especially if edf is close to k'.
#>
#> k' edf k-index p-value
#> s(spei_12m) 9.00 8.74 1 0.81
#> s(gdp_per_capita) 9.00 8.95 1 0.80
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.Code
data |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam(
model = maper_mpepr_gam_2,
type = 2,
x_label = "Standardised Precipitation Evapotranspiration Index (12 months)",
y_label = "Predicted probability of MAPER & MPEPR"
)maper_mpepr_gam_2 model. All other variables are held constant at their mean values except SPEI. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
By s(spei_12m) + s(gdp_per_capita) + year (Unordered year)
In this model, the year variable is treated as a unordered categorical variable.
mbepr_gam_3 |> summary()
#>
#> Family: Beta regression(20.626)
#> Link function: logit
#>
#> Formula:
#> mbepr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.17751855 0.01264439 -251.29862 < 2.22e-16 ***
#> year2009 0.21946564 0.01606210 13.66357 < 2.22e-16 ***
#> year2011 0.26972212 0.01595683 16.90324 < 2.22e-16 ***
#> year2012 0.16521320 0.01756187 9.40749 < 2.22e-16 ***
#> year2013 0.37280450 0.01608782 23.17309 < 2.22e-16 ***
#> year2014 0.43539213 0.01645695 26.45643 < 2.22e-16 ***
#> year2015 0.34933198 0.01765053 19.79158 < 2.22e-16 ***
#> year2016 0.41030039 0.01827290 22.45404 < 2.22e-16 ***
#> year2017 0.41180257 0.01779022 23.14769 < 2.22e-16 ***
#> year2018 0.39845137 0.01772076 22.48500 < 2.22e-16 ***
#> year2019 0.38061511 0.01832153 20.77420 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 8.590172 8.953754 260.0321 < 2.22e-16 ***
#> s(gdp_per_capita) 8.948270 8.999109 6695.3422 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0361 Deviance explained = 12.6%
#> -REML = -1.1223e+05 Scale est. = 1 n = 57487Code
mbepr_gam_3 model.
| Value | Interpretation | Rule | |
|---|---|---|---|
| R2 | 0.0361097497 | weak | cohen1988 |
| SE | 0.0014621212 | NA | NA |
| Lower CI | 0.0332440448 | weak | cohen1988 |
| Upper CI | 0.0389754546 | weak | cohen1988 |
Source: Created by the authors.
Code
mbepr_gam_3 |>
broom::glance() |>
tidyr::pivot_longer(dplyr::everything()) |>
md_named_tibble()mbepr_gam_3 model.
| Value | |
|---|---|
| df | 28.5384421900 |
| logLik | 112328.7929502070 |
| AIC | -224597.6801733562 |
| BIC | -224329.3230603794 |
| deviance | 59160.0001780340 |
| df.residual | 57458.4615578100 |
| nobs | 57487.0000000000 |
| adj.r.squared | 0.0361097497 |
| npar | 29.0000000000 |
Source: Created by the authors.
Code
mbepr_gam_3 |>
summarise_coefs() |>
md_named_tibble()mbepr_gam_3 model.
| Value | |
|---|---|
| [Mean] | -0.2877731315 |
| (Intercept) | -3.1775185491 |
| year2009 | 0.2194656411 |
| year2011 | 0.2697221198 |
| year2012 | 0.1652131985 |
| year2013 | 0.3728045007 |
| year2014 | 0.4353921284 |
| year2015 | 0.3493319752 |
| year2016 | 0.4103003866 |
| year2017 | 0.4118025670 |
| year2018 | 0.3984513695 |
| year2019 | 0.3806151101 |
| mean(s(spei_12m)) | -0.0268823140 |
| mean(s(gdp_per_capita)) | -0.9265622705 |
Source: Created by the authors.
Code
mbepr_gam_3 |> mgcViz::getViz() |> mgcViz::check.gamViz()
#>
#> Method: REML Optimizer: outer newton
#> full convergence after 6 iterations.
#> Gradient range [-0.000000007552963588,0.0001310561095]
#> (score -112229.4703 & scale 1).
#> Hessian positive definite, eigenvalue range [2.742501638,24607.56655].
#> Model rank = 29 / 29
#>
#> Basis dimension (k) checking results. Low p-value (k-index<1) may
#> indicate that k is too low, especially if edf is close to k'.
#>
#> k' edf k-index p-value
#> s(spei_12m) 9.00 8.59 1.00 0.51
#> s(gdp_per_capita) 9.00 8.95 0.99 0.30
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.Code
dplyr::mutate(data, year = factor(year, ordered = FALSE)) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam(
model = mbepr_gam_3,
type = 3,
x_label = "Standardised Precipitation Evapotranspiration Index (12 months)",
y_label = "Predicted probability of MBEPR"
)mbepr_gam_3 model. All other variables are held constant at their mean values except SPEI. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
beipr_gam_3 |> summary()
#>
#> Family: Beta regression(29.757)
#> Link function: logit
#>
#> Formula:
#> beipr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.91671409 0.01058283 -275.60826 < 2.22e-16 ***
#> year2009 0.12774769 0.01345866 9.49186 < 2.22e-16 ***
#> year2011 0.15064247 0.01342023 11.22503 < 2.22e-16 ***
#> year2012 0.07558004 0.01481980 5.09994 0.00000033977 ***
#> year2013 0.24903905 0.01351495 18.42693 < 2.22e-16 ***
#> year2014 0.28428158 0.01387911 20.48269 < 2.22e-16 ***
#> year2015 0.32345451 0.01474256 21.94019 < 2.22e-16 ***
#> year2016 0.28846946 0.01539833 18.73381 < 2.22e-16 ***
#> year2017 0.36147514 0.01485394 24.33531 < 2.22e-16 ***
#> year2018 0.38314312 0.01476064 25.95709 < 2.22e-16 ***
#> year2019 0.36490532 0.01528446 23.87427 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 8.087818 8.785738 129.7223 < 2.22e-16 ***
#> s(gdp_per_capita) 8.963470 8.999553 6882.1263 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0631 Deviance explained = 12.3%
#> -REML = -1.0766e+05 Scale est. = 1 n = 57487Code
beipr_gam_3 model.
| Value | Interpretation | Rule | |
|---|---|---|---|
| R2 | 0.0631125811 | weak | cohen1988 |
| SE | 0.0018788362 | NA | NA |
| Lower CI | 0.0594301298 | weak | cohen1988 |
| Upper CI | 0.0667950325 | weak | cohen1988 |
Source: Created by the authors.
Code
beipr_gam_3 |>
broom::glance() |>
tidyr::pivot_longer(dplyr::everything()) |>
md_named_tibble()beipr_gam_3 model.
| Value | |
|---|---|
| df | 28.0512885520 |
| logLik | 107759.0063622698 |
| AIC | -215458.5539124882 |
| BIC | -215192.1988254731 |
| deviance | 58635.8529103912 |
| df.residual | 57458.9487114480 |
| nobs | 57487.0000000000 |
| adj.r.squared | 0.0631125811 |
| npar | 29.0000000000 |
Source: Created by the authors.
Code
beipr_gam_3 |>
summarise_coefs() |>
md_named_tibble()beipr_gam_3 model.
| Value | |
|---|---|
| [Mean] | -0.2766509191 |
| (Intercept) | -2.9167140924 |
| year2009 | 0.1277476919 |
| year2011 | 0.1506424680 |
| year2012 | 0.0755800367 |
| year2013 | 0.2490390471 |
| year2014 | 0.2842815840 |
| year2015 | 0.3234545123 |
| year2016 | 0.2884694561 |
| year2017 | 0.3614751356 |
| year2018 | 0.3831431248 |
| year2019 | 0.3649053222 |
| mean(s(spei_12m)) | -0.0761424849 |
| mean(s(gdp_per_capita)) | -0.7810687308 |
Source: Created by the authors.
Code
beipr_gam_3 |> mgcViz::getViz() |> mgcViz::check.gamViz()
#>
#> Method: REML Optimizer: outer newton
#> full convergence after 5 iterations.
#> Gradient range [0.00000007628265752,0.0008694512423]
#> (score -107659.7478 & scale 1).
#> Hessian positive definite, eigenvalue range [2.587987234,26850.58834].
#> Model rank = 29 / 29
#>
#> Basis dimension (k) checking results. Low p-value (k-index<1) may
#> indicate that k is too low, especially if edf is close to k'.
#>
#> k' edf k-index p-value
#> s(spei_12m) 9.00 8.09 0.96 0.03 *
#> s(gdp_per_capita) 9.00 8.96 0.97 0.07 .
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.Code
dplyr::mutate(data, year = factor(year, ordered = FALSE)) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam(
model = beipr_gam_3,
type = 3,
x_label = "Standardised Precipitation Evapotranspiration Index (12 months)",
y_label = "Predicted probability of BEIPR"
)beipr_gam_3 model. All other variables are held constant at their mean values except SPEI. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
mbepr_beipr_gam_3 |> summary()
#>
#> Family: Beta regression(18.821)
#> Link function: logit
#>
#> Formula:
#> mbepr_beipr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.18114506 0.01018210 -214.21360 < 2.22e-16 ***
#> year2009 0.14925652 0.01295454 11.52156 < 2.22e-16 ***
#> year2011 0.14163298 0.01292342 10.95940 < 2.22e-16 ***
#> year2012 0.06000637 0.01428716 4.20002 0.000026689 ***
#> year2013 0.21463584 0.01306667 16.42621 < 2.22e-16 ***
#> year2014 0.26260938 0.01340196 19.59485 < 2.22e-16 ***
#> year2015 0.22481585 0.01434108 15.67636 < 2.22e-16 ***
#> year2016 0.22643036 0.01491051 15.18596 < 2.22e-16 ***
#> year2017 0.26048463 0.01444929 18.02750 < 2.22e-16 ***
#> year2018 0.26291844 0.01438755 18.27403 < 2.22e-16 ***
#> year2019 0.25599396 0.01487603 17.20849 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 7.619617 8.538673 121.8412 < 2.22e-16 ***
#> s(gdp_per_capita) 8.962548 8.999531 6728.9094 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0903 Deviance explained = 12.2%
#> -REML = -75869 Scale est. = 1 n = 57487Code
mbepr_beipr_gam_3 model.
| Value | Interpretation | Rule | |
|---|---|---|---|
| R2 | 0.0902584119 | weak | cohen1988 |
| SE | 0.0021817523 | NA | NA |
| Lower CI | 0.0859822559 | weak | cohen1988 |
| Upper CI | 0.0945345678 | weak | cohen1988 |
Source: Created by the authors.
Code
mbepr_beipr_gam_3 |>
broom::glance() |>
tidyr::pivot_longer(dplyr::everything()) |>
md_named_tibble()mbepr_beipr_gam_3 model.
| Value | |
|---|---|
| df | 27.5821646294 |
| logLik | 75966.5942130833 |
| AIC | -151874.1120177862 |
| BIC | -151609.4699680747 |
| deviance | 56843.8939035902 |
| df.residual | 57459.4178353706 |
| nobs | 57487.0000000000 |
| adj.r.squared | 0.0902584119 |
| npar | 29.0000000000 |
Source: Created by the authors.
Code
mbepr_beipr_gam_3 |>
summarise_coefs() |>
md_named_tibble()mbepr_beipr_gam_3 model.
| Value | |
|---|---|
| [Mean] | -0.2557029687 |
| (Intercept) | -2.1811450599 |
| year2009 | 0.1492565233 |
| year2011 | 0.1416329845 |
| year2012 | 0.0600063687 |
| year2013 | 0.2146358442 |
| year2014 | 0.2626093801 |
| year2015 | 0.2248158540 |
| year2016 | 0.2264303616 |
| year2017 | 0.2604846318 |
| year2018 | 0.2629184427 |
| year2019 | 0.2559939591 |
| mean(s(spei_12m)) | -0.0366551981 |
| mean(s(gdp_per_capita)) | -0.7736809556 |
Source: Created by the authors.
Code
mbepr_beipr_gam_3 |> mgcViz::getViz() |> mgcViz::check.gamViz()
#>
#> Method: REML Optimizer: outer newton
#> full convergence after 8 iterations.
#> Gradient range [-0.0001292059843,0.0003324216679]
#> (score -75869.3646 & scale 1).
#> Hessian positive definite, eigenvalue range [1.430426406,28213.15345].
#> Model rank = 29 / 29
#>
#> Basis dimension (k) checking results. Low p-value (k-index<1) may
#> indicate that k is too low, especially if edf is close to k'.
#>
#> k' edf k-index p-value
#> s(spei_12m) 9.00 7.62 0.99 0.4
#> s(gdp_per_capita) 9.00 8.96 1.00 0.7
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.Code
dplyr::mutate(data, year = factor(year, ordered = FALSE)) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam(
model = mbepr_beipr_gam_3,
type = 3,
x_label = "Standardised Precipitation Evapotranspiration Index (12 months)",
y_label = "Predicted probability of MBEPR & BEIPR"
)mbepr_beipr_gam_3 model. All other variables are held constant at their mean values except SPEI. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
maper_gam_3 |> summary()
#>
#> Family: Beta regression(30.068)
#> Link function: logit
#>
#> Formula:
#> maper ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -4.03156418 0.01371885 -293.87048 < 2.22e-16 ***
#> year2009 0.18134814 0.01763039 10.28611 < 2.22e-16 ***
#> year2011 0.27855200 0.01740199 16.00690 < 2.22e-16 ***
#> year2012 0.08872108 0.01911000 4.64265 0.0000034396 ***
#> year2013 0.40296993 0.01748521 23.04634 < 2.22e-16 ***
#> year2014 0.40124539 0.01802165 22.26463 < 2.22e-16 ***
#> year2015 0.35389354 0.01918292 18.44836 < 2.22e-16 ***
#> year2016 0.39620418 0.01989293 19.91683 < 2.22e-16 ***
#> year2017 0.46231172 0.01927478 23.98532 < 2.22e-16 ***
#> year2018 0.29859262 0.01940672 15.38604 < 2.22e-16 ***
#> year2019 0.27944209 0.02004991 13.93732 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 8.694710 8.973967 664.9771 < 2.22e-16 ***
#> s(gdp_per_capita) 8.944671 8.998983 7907.9297 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0196 Deviance explained = 15.5%
#> -REML = -1.6567e+05 Scale est. = 1 n = 57487Code
maper_gam_3 model.
| Value | Interpretation | Rule | |
|---|---|---|---|
| R2 | 0.0195525479 | very weak (negligible) | cohen1988 |
| SE | 0.0010943835 | NA | NA |
| Lower CI | 0.0174075956 | very weak (negligible) | cohen1988 |
| Upper CI | 0.0216975002 | weak | cohen1988 |
Source: Created by the authors.
Code
maper_gam_3 |>
broom::glance() |>
tidyr::pivot_longer(dplyr::everything()) |>
md_named_tibble()maper_gam_3 model.
| Value | |
|---|---|
| df | 28.6393814172 |
| logLik | 165771.6188545161 |
| AIC | -331483.2918093869 |
| BIC | -331214.7547369944 |
| deviance | 61106.8873587697 |
| df.residual | 57458.3606185828 |
| nobs | 57487.0000000000 |
| adj.r.squared | 0.0195525479 |
| npar | 29.0000000000 |
Source: Created by the authors.
Code
maper_gam_3 |>
summarise_coefs() |>
md_named_tibble()maper_gam_3 model.
| Value | |
|---|---|
| [Mean] | -0.3735969657 |
| (Intercept) | -4.0315641827 |
| year2009 | 0.1813481356 |
| year2011 | 0.2785519963 |
| year2012 | 0.0887210850 |
| year2013 | 0.4029699259 |
| year2014 | 0.4012453852 |
| year2015 | 0.3538935373 |
| year2016 | 0.3962041771 |
| year2017 | 0.4623117250 |
| year2018 | 0.2985926161 |
| year2019 | 0.2794420880 |
| mean(s(spei_12m)) | -0.0515535149 |
| mean(s(gdp_per_capita)) | -1.0535607621 |
Source: Created by the authors.
Code
maper_gam_3 |> mgcViz::getViz() |> mgcViz::check.gamViz()
#>
#> Method: REML Optimizer: outer newton
#> full convergence after 6 iterations.
#> Gradient range [-0.000002867503382,0.127225218]
#> (score -165672.2724 & scale 1).
#> Hessian positive definite, eigenvalue range [3.108890111,20555.5479].
#> Model rank = 29 / 29
#>
#> Basis dimension (k) checking results. Low p-value (k-index<1) may
#> indicate that k is too low, especially if edf is close to k'.
#>
#> k' edf k-index p-value
#> s(spei_12m) 9.00 8.69 1.01 0.83
#> s(gdp_per_capita) 9.00 8.94 1.00 0.67
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.Code
dplyr::mutate(data, year = factor(year, ordered = FALSE)) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam(
model = maper_gam_3,
type = 3,
x_label = "Standardised Precipitation Evapotranspiration Index (12 months)",
y_label = "Predicted probability of MAPER"
)maper_gam_3 model. All other variables are held constant at their mean values except SPEI. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
mpepr_gam_3 |> summary()
#>
#> Family: Beta regression(37.457)
#> Link function: logit
#>
#> Formula:
#> mpepr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.88113475 0.01274667 -304.48226 < 2.22e-16 ***
#> year2009 0.16202699 0.01633782 9.91730 < 2.22e-16 ***
#> year2011 0.28188199 0.01608819 17.52105 < 2.22e-16 ***
#> year2012 0.11860212 0.01763071 6.72702 0.000000000017317 ***
#> year2013 0.33552317 0.01624424 20.65490 < 2.22e-16 ***
#> year2014 0.31509842 0.01677777 18.78071 < 2.22e-16 ***
#> year2015 0.35076953 0.01772842 19.78571 < 2.22e-16 ***
#> year2016 0.38552502 0.01837166 20.98477 < 2.22e-16 ***
#> year2017 0.50147159 0.01769887 28.33354 < 2.22e-16 ***
#> year2018 0.40074422 0.01779105 22.52505 < 2.22e-16 ***
#> year2019 0.33907330 0.01845077 18.37719 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 8.647503 8.965450 822.0245 < 2.22e-16 ***
#> s(gdp_per_capita) 8.951176 8.999205 7986.3431 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.00384 Deviance explained = 16.1%
#> -REML = -1.5263e+05 Scale est. = 1 n = 57487Code
mpepr_gam_3 model.
| Value | Interpretation | Rule | |
|---|---|---|---|
| R2 | 0.0038386871 | very weak (negligible) | cohen1988 |
| SE | 0.0004926796 | NA | NA |
| Lower CI | 0.0028730528 | very weak (negligible) | cohen1988 |
| Upper CI | 0.0048043214 | very weak (negligible) | cohen1988 |
Source: Created by the authors.
Code
mpepr_gam_3 |>
broom::glance() |>
tidyr::pivot_longer(dplyr::everything()) |>
md_named_tibble()mpepr_gam_3 model.
| Value | |
|---|---|
| df | 28.5986793746 |
| logLik | 152726.7044215837 |
| AIC | -305393.4795328700 |
| BIC | -305125.0167750675 |
| deviance | 61538.8824296946 |
| df.residual | 57458.4013206254 |
| nobs | 57487.0000000000 |
| adj.r.squared | 0.0038386871 |
| npar | 29.0000000000 |
Source: Created by the authors.
Code
mpepr_gam_3 |>
summarise_coefs() |>
md_named_tibble()mpepr_gam_3 model.
| Value | |
|---|---|
| [Mean] | -0.3372013358 |
| (Intercept) | -3.8811347527 |
| year2009 | 0.1620269881 |
| year2011 | 0.2818819858 |
| year2012 | 0.1186021185 |
| year2013 | 0.3355231690 |
| year2014 | 0.3150984234 |
| year2015 | 0.3507695348 |
| year2016 | 0.3855250165 |
| year2017 | 0.5014715862 |
| year2018 | 0.4007442183 |
| year2019 | 0.3390733003 |
| mean(s(spei_12m)) | -0.0288333047 |
| mean(s(gdp_per_capita)) | -0.9809911760 |
Source: Created by the authors.
Code
mpepr_gam_3 |> mgcViz::getViz() |> mgcViz::check.gamViz()
#>
#> Method: REML Optimizer: outer newton
#> full convergence after 5 iterations.
#> Gradient range [-0.00001519267568,0.03105131563]
#> (score -152626.3641 & scale 1).
#> Hessian positive definite, eigenvalue range [2.990365667,23167.47384].
#> Model rank = 29 / 29
#>
#> Basis dimension (k) checking results. Low p-value (k-index<1) may
#> indicate that k is too low, especially if edf is close to k'.
#>
#> k' edf k-index p-value
#> s(spei_12m) 9.00 8.65 0.98 0.095 .
#> s(gdp_per_capita) 9.00 8.95 0.98 0.125
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.Code
dplyr::mutate(data, year = factor(year, ordered = FALSE)) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam(
model = mpepr_gam_3,
type = 3,
x_label = "Standardised Precipitation Evapotranspiration Index (12 months)",
y_label = "Predicted probability of MPEPR"
)mpepr_gam_3 model. All other variables are held constant at their mean values except SPEI. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
maper_mpepr_gam_3 |> summary()
#>
#> Family: Beta regression(24.906)
#> Link function: logit
#>
#> Formula:
#> maper_mpepr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.15491009 0.01203117 -262.22794 < 2.22e-16 ***
#> year2009 0.16017953 0.01535889 10.42911 < 2.22e-16 ***
#> year2011 0.22423453 0.01521530 14.73743 < 2.22e-16 ***
#> year2012 0.07695023 0.01670604 4.60613 0.0000041023 ***
#> year2013 0.28868238 0.01535012 18.80652 < 2.22e-16 ***
#> year2014 0.27339208 0.01584927 17.24951 < 2.22e-16 ***
#> year2015 0.26100119 0.01686041 15.48012 < 2.22e-16 ***
#> year2016 0.30722661 0.01745822 17.59782 < 2.22e-16 ***
#> year2017 0.40370221 0.01683132 23.98517 < 2.22e-16 ***
#> year2018 0.24364451 0.01701131 14.32250 < 2.22e-16 ***
#> year2019 0.21289143 0.01759856 12.09710 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 8.739492 8.980914 782.5095 < 2.22e-16 ***
#> s(gdp_per_capita) 8.945937 8.999029 7854.0728 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0487 Deviance explained = 16.1%
#> -REML = -1.1674e+05 Scale est. = 1 n = 57487Code
maper_mpepr_gam_3 model.
| Value | Interpretation | Rule | |
|---|---|---|---|
| R2 | 0.0487055780 | weak | cohen1988 |
| SE | 0.0016758990 | NA | NA |
| Lower CI | 0.0454208762 | weak | cohen1988 |
| Upper CI | 0.0519902797 | weak | cohen1988 |
Source: Created by the authors.
Code
maper_mpepr_gam_3 |>
broom::glance() |>
tidyr::pivot_longer(dplyr::everything()) |>
md_named_tibble()maper_mpepr_gam_3 model.
| Value | |
|---|---|
| df | 28.685429756 |
| logLik | 116845.724333433 |
| AIC | -233631.488781631 |
| BIC | -233362.889058591 |
| deviance | 59536.185150791 |
| df.residual | 57458.314570244 |
| nobs | 57487.000000000 |
| adj.r.squared | 0.048705578 |
| npar | 29.000000000 |
Source: Created by the authors.
Code
maper_mpepr_gam_3 |>
summarise_coefs() |>
md_named_tibble()maper_mpepr_gam_3 model.
| Value | |
|---|---|
| [Mean] | -0.3055395111 |
| (Intercept) | -3.1549100891 |
| year2009 | 0.1601795330 |
| year2011 | 0.2242345324 |
| year2012 | 0.0769502297 |
| year2013 | 0.2886823754 |
| year2014 | 0.2733920755 |
| year2015 | 0.2610011857 |
| year2016 | 0.3072266135 |
| year2017 | 0.4037022116 |
| year2018 | 0.2436445091 |
| year2019 | 0.2128914320 |
| mean(s(spei_12m)) | 0.0017632820 |
| mean(s(gdp_per_capita)) | -0.9081677744 |
Source: Created by the authors.
Code
maper_mpepr_gam_3 |> mgcViz::getViz() |> mgcViz::check.gamViz()
#>
#> Method: REML Optimizer: outer newton
#> full convergence after 5 iterations.
#> Gradient range [0.000000006064042157,0.0004676518947]
#> (score -116743.8866 & scale 1).
#> Hessian positive definite, eigenvalue range [3.173550905,25060.67586].
#> Model rank = 29 / 29
#>
#> Basis dimension (k) checking results. Low p-value (k-index<1) may
#> indicate that k is too low, especially if edf is close to k'.
#>
#> k' edf k-index p-value
#> s(spei_12m) 9.00 8.74 1.00 0.45
#> s(gdp_per_capita) 9.00 8.95 0.98 0.09 .
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.Code
dplyr::mutate(data, year = factor(year, ordered = FALSE)) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam(
model = maper_mpepr_gam_3,
type = 3,
x_label = "Standardised Precipitation Evapotranspiration Index (12 months)",
y_label = "Predicted probability of MAPER & MPEPR"
)maper_mpepr_gam_3 model. All other variables are held constant at their mean values except SPEI. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
By s(year) (Continuous year)
Code
mbepr_gam_4 <- mgcv::gam(
mbepr ~ s(year),
data = dplyr::mutate(data, year = as.integer(as.character(year))),
family = mgcv::betar(link = "logit"),
method = "REML"
)mbepr_gam_4 |> summary()
#>
#> Family: Beta regression(17.632)
#> Link function: logit
#>
#> Formula:
#> mbepr ~ s(year)
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.819223463 0.003244516 -868.9196 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(year) 8.517735 8.935257 302.3165 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = -0.00359 Deviance explained = 0.499%
#> -REML = -1.1796e+05 Scale est. = 1 n = 62762Code
mbepr_gam_4 |>
summarise_r2(
dplyr::mutate(data, year = as.integer(as.character(year))) |>
nrow()
) |>
md_named_tibble()mbepr_gam_4 model.
| Value | Interpretation | Rule | |
|---|---|---|---|
| R2 | 0 | no effect | cohen1988 |
| SE | 0 | NA | NA |
| Lower CI | 0 | no effect | cohen1988 |
| Upper CI | 0 | no effect | cohen1988 |
Source: Created by the authors.
Code
mbepr_gam_4 |>
broom::glance() |>
tidyr::pivot_longer(dplyr::everything()) |>
md_named_tibble()mbepr_gam_4 model.
| Value | |
|---|---|
| df | 9.5177348799 |
| logLik | 117986.4920079141 |
| AIC | -235951.1135022862 |
| BIC | -235852.1810852699 |
| deviance | 64482.0026382929 |
| df.residual | 62752.4822651201 |
| nobs | 62762.0000000000 |
| adj.r.squared | -0.0035886584 |
| npar | 10.0000000000 |
Source: Created by the authors.
Code
mbepr_gam_4 |>
summarise_coefs() |>
md_named_tibble()mbepr_gam_4 model.
| Value | |
|---|---|
| [Mean] | -0.2591799301 |
| (Intercept) | -2.8192234633 |
| mean(s(year)) | 0.0252693513 |
Source: Created by the authors.
Code
mbepr_gam_4 |> mgcViz::getViz() |> mgcViz::check.gamViz()
#>
#> Method: REML Optimizer: outer newton
#> full convergence after 6 iterations.
#> Gradient range [-0.0000007308610019,0.03364194555]
#> (score -117956.7533 & scale 1).
#> Hessian positive definite, eigenvalue range [3.531791006,26569.1772].
#> Model rank = 10 / 10
#>
#> Basis dimension (k) checking results. Low p-value (k-index<1) may
#> indicate that k is too low, especially if edf is close to k'.
#>
#> k' edf k-index p-value
#> s(year) 9.00 8.52 0.98 0.23
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.Code
dplyr::mutate(data, year = as.integer(as.character(year))) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam(
model = mbepr_gam_4,
type = 4,
x_label = "Years",
y_label = "Predicted probability of MBEPR"
)mbepr_gam_4 model. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
Code
beipr_gam_4 <- mgcv::gam(
beipr ~ s(year),
data = dplyr::mutate(data, year = as.integer(as.character(year))),
family = mgcv::betar(link = "logit"),
method = "REML"
)beipr_gam_4 |> summary()
#>
#> Family: Beta regression(25.787)
#> Link function: logit
#>
#> Formula:
#> beipr ~ s(year)
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.648641361 0.002748208 -963.7703 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(year) 8.380103 8.894804 281.1438 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = -0.00755 Deviance explained = 0.486%
#> -REML = -1.1332e+05 Scale est. = 1 n = 62762Code
beipr_gam_4 |>
summarise_r2(
dplyr::mutate(data, year = as.integer(as.character(year))) |>
nrow()
) |>
md_named_tibble()beipr_gam_4 model.
| Value | Interpretation | Rule | |
|---|---|---|---|
| R2 | 0 | no effect | cohen1988 |
| SE | 0 | NA | NA |
| Lower CI | 0 | no effect | cohen1988 |
| Upper CI | 0 | no effect | cohen1988 |
Source: Created by the authors.
Code
beipr_gam_4 |>
broom::glance() |>
tidyr::pivot_longer(dplyr::everything()) |>
md_named_tibble()beipr_gam_4 model.
| Value | |
|---|---|
| df | 9.3801031575 |
| logLik | 113351.7302965717 |
| AIC | -226681.8554885659 |
| BIC | -226584.1236629445 |
| deviance | 63829.0813461868 |
| df.residual | 62752.6198968425 |
| nobs | 62762.0000000000 |
| adj.r.squared | -0.0075487984 |
| npar | 10.0000000000 |
Source: Created by the authors.
Code
beipr_gam_4 |>
summarise_coefs() |>
md_named_tibble()beipr_gam_4 model.
| Value | |
|---|---|
| [Mean] | -0.2736261600 |
| (Intercept) | -2.6486413607 |
| mean(s(year)) | -0.0097355821 |
Source: Created by the authors.
Code
beipr_gam_4 |> mgcViz::getViz() |> mgcViz::check.gamViz()
#>
#> Method: REML Optimizer: outer newton
#> full convergence after 6 iterations.
#> Gradient range [-0.0000000004378528651,0.00001056270043]
#> (score -113322.8181 & scale 1).
#> Hessian positive definite, eigenvalue range [3.395724488,29159.85227].
#> Model rank = 10 / 10
#>
#> Basis dimension (k) checking results. Low p-value (k-index<1) may
#> indicate that k is too low, especially if edf is close to k'.
#>
#> k' edf k-index p-value
#> s(year) 9.00 8.38 1.01 0.92
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.Code
dplyr::mutate(data, year = as.integer(as.character(year))) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam(
model = beipr_gam_4,
type = 4,
x_label = "Years",
y_label = "Predicted probability of BEIPR"
)beipr_gam_4 model. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
Code
mbepr_beipr_gam_4 <- mgcv::gam(
mbepr_beipr ~ s(year),
data = dplyr::mutate(data, year = as.integer(as.character(year))),
family = mgcv::betar(link = "logit"),
method = "REML"
)mbepr_beipr_gam_4 |> summary()
#>
#> Family: Beta regression(16.293)
#> Link function: logit
#>
#> Formula:
#> mbepr_beipr ~ s(year)
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -1.96506495 0.00268522 -731.8079 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(year) 8.44098 8.913794 235.0998 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0045 Deviance explained = 0.392%
#> -REML = -78452 Scale est. = 1 n = 62762Code
mbepr_beipr_gam_4 |>
summarise_r2(
dplyr::mutate(data, year = as.integer(as.character(year))) |>
nrow()
) |>
md_named_tibble()mbepr_beipr_gam_4 model.
| Value | Interpretation | Rule | |
|---|---|---|---|
| R2 | 0.0045000402 | very weak (negligible) | cohen1988 |
| SE | 0.0005330977 | NA | NA |
| Lower CI | 0.0034551879 | very weak (negligible) | cohen1988 |
| Upper CI | 0.0055448926 | very weak (negligible) | cohen1988 |
Source: Created by the authors.
Code
mbepr_beipr_gam_4 |>
broom::glance() |>
tidyr::pivot_longer(dplyr::everything()) |>
md_named_tibble()mbepr_beipr_gam_4 model.
| Value | |
|---|---|
| df | 9.4409801854 |
| logLik | 78481.3360960384 |
| AIC | -156941.1983968910 |
| BIC | -156844.0605562020 |
| deviance | 61788.3616920760 |
| df.residual | 62752.5590198146 |
| nobs | 62762.0000000000 |
| adj.r.squared | 0.0045000402 |
| npar | 10.0000000000 |
Source: Created by the authors.
Code
mbepr_beipr_gam_4 |>
summarise_coefs() |>
md_named_tibble()mbepr_beipr_gam_4 model.
| Value | |
|---|---|
| [Mean] | -0.1919132142 |
| (Intercept) | -1.9650649515 |
| mean(s(year)) | 0.0051036454 |
Source: Created by the authors.
Code
mbepr_beipr_gam_4 |> mgcViz::getViz() |> mgcViz::check.gamViz()
#>
#> Method: REML Optimizer: outer newton
#> full convergence after 4 iterations.
#> Gradient range [0.0001485521986,0.01425683628]
#> (score -78451.89082 & scale 1).
#> Hessian positive definite, eigenvalue range [3.542988508,30825.81986].
#> Model rank = 10 / 10
#>
#> Basis dimension (k) checking results. Low p-value (k-index<1) may
#> indicate that k is too low, especially if edf is close to k'.
#>
#> k' edf k-index p-value
#> s(year) 9.00 8.44 0.98 0.17
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.Code
dplyr::mutate(data, year = as.integer(as.character(year))) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam(
model = mbepr_beipr_gam_4,
type = 4,
x_label = "Years",
y_label = "Predicted probability of MBEPR & BEIPR"
)mbepr_beipr_gam_4 model. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
Code
maper_gam_4 <- mgcv::gam(
maper ~ s(year),
data = dplyr::mutate(data, year = as.integer(as.character(year))),
family = mgcv::betar(link = "logit"),
method = "REML"
)maper_gam_4 |> summary()
#>
#> Family: Beta regression(24.478)
#> Link function: logit
#>
#> Formula:
#> maper ~ s(year)
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.670795216 0.003547555 -1034.739 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(year) 8.587611 8.952185 318.7632 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = -0.00151 Deviance explained = 0.488%
#> -REML = -1.7521e+05 Scale est. = 1 n = 62762Code
maper_gam_4 |>
summarise_r2(
dplyr::mutate(data, year = as.integer(as.character(year))) |>
nrow()
) |>
md_named_tibble()maper_gam_4 model.
| Value | Interpretation | Rule | |
|---|---|---|---|
| R2 | 0 | no effect | cohen1988 |
| SE | 0 | NA | NA |
| Lower CI | 0 | no effect | cohen1988 |
| Upper CI | 0 | no effect | cohen1988 |
Source: Created by the authors.
Code
maper_gam_4 |>
broom::glance() |>
tidyr::pivot_longer(dplyr::everything()) |>
md_named_tibble()maper_gam_4 model.
| Value | |
|---|---|
| df | 9.5876109295 |
| logLik | 175244.4552867728 |
| AIC | -350467.0062043938 |
| BIC | -350367.9206397486 |
| deviance | 67164.5053157659 |
| df.residual | 62752.4123890705 |
| nobs | 62762.0000000000 |
| adj.r.squared | -0.0015113762 |
| npar | 10.0000000000 |
Source: Created by the authors.
Code
maper_gam_4 |>
summarise_coefs() |>
md_named_tibble()maper_gam_4 model.
| Value | |
|---|---|
| [Mean] | -0.3262673232 |
| (Intercept) | -3.6707952155 |
| mean(s(year)) | 0.0453468870 |
Source: Created by the authors.
Code
maper_gam_4 |> mgcViz::getViz() |> mgcViz::check.gamViz()
#>
#> Method: REML Optimizer: outer newton
#> full convergence after 5 iterations.
#> Gradient range [-0.000001789168296,0.1457289897]
#> (score -175214.1738 & scale 1).
#> Hessian positive definite, eigenvalue range [3.266969182,21653.71035].
#> Model rank = 10 / 10
#>
#> Basis dimension (k) checking results. Low p-value (k-index<1) may
#> indicate that k is too low, especially if edf is close to k'.
#>
#> k' edf k-index p-value
#> s(year) 9.00 8.59 1 0.43
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.Code
dplyr::mutate(data, year = as.integer(as.character(year))) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam(
model = maper_gam_4,
type = 4,
x_label = "Years",
y_label = "Predicted probability of MAPER"
)maper_gam_4 model. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
Code
mpepr_gam_4 <- mgcv::gam(
mpepr ~ s(year),
data = dplyr::mutate(data, year = as.integer(as.character(year))),
family = mgcv::betar(link = "logit"),
method = "REML"
)mpepr_gam_4 |> summary()
#>
#> Family: Beta regression(30.596)
#> Link function: logit
#>
#> Formula:
#> mpepr ~ s(year)
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.530426653 0.003291301 -1072.654 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(year) 8.125824 8.797382 452.6992 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = -0.0126 Deviance explained = 0.688%
#> -REML = -1.6103e+05 Scale est. = 1 n = 62762Code
mpepr_gam_4 |>
summarise_r2(
dplyr::mutate(data, year = as.integer(as.character(year))) |>
nrow()
) |>
md_named_tibble()mpepr_gam_4 model.
| Value | Interpretation | Rule | |
|---|---|---|---|
| R2 | 0 | no effect | cohen1988 |
| SE | 0 | NA | NA |
| Lower CI | 0 | no effect | cohen1988 |
| Upper CI | 0 | no effect | cohen1988 |
Source: Created by the authors.
Code
mpepr_gam_4 |>
broom::glance() |>
tidyr::pivot_longer(dplyr::everything()) |>
md_named_tibble()mpepr_gam_4 model.
| Value | |
|---|---|
| df | 9.125823871 |
| logLik | 161057.642508866 |
| AIC | -322093.690254409 |
| BIC | -321996.005207994 |
| deviance | 67280.102592947 |
| df.residual | 62752.874176129 |
| nobs | 62762.000000000 |
| adj.r.squared | -0.012590109 |
| npar | 10.000000000 |
Source: Created by the authors.
Code
mpepr_gam_4 |>
summarise_coefs() |>
md_named_tibble()mpepr_gam_4 model.
| Value | |
|---|---|
| [Mean] | -0.3632127806 |
| (Intercept) | -3.5304266535 |
| mean(s(year)) | -0.0113001281 |
Source: Created by the authors.
Code
mpepr_gam_4 |> mgcViz::getViz() |> mgcViz::check.gamViz()
#>
#> Method: REML Optimizer: outer newton
#> full convergence after 5 iterations.
#> Gradient range [0.0000409648117,0.009724409113]
#> (score -161030.7811 & scale 1).
#> Hessian positive definite, eigenvalue range [3.051833023,24661.20026].
#> Model rank = 10 / 10
#>
#> Basis dimension (k) checking results. Low p-value (k-index<1) may
#> indicate that k is too low, especially if edf is close to k'.
#>
#> k' edf k-index p-value
#> s(year) 9.00 8.13 1 0.56
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.Code
dplyr::mutate(data, year = as.integer(as.character(year))) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam(
model = mpepr_gam_4,
type = 4,
x_label = "Years",
y_label = "Predicted probability of MPEPR"
)mpepr_gam_4 model. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
Code
maper_mpepr_gam_4 <- mgcv::gam(
maper_mpepr ~ s(year),
data = dplyr::mutate(data, year = as.integer(as.character(year))),
family = mgcv::betar(link = "logit"),
method = "REML"
)maper_mpepr_gam_4 |> summary()
#>
#> Family: Beta regression(20.399)
#> Link function: logit
#>
#> Formula:
#> maper_mpepr ~ s(year)
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.877019036 0.003155272 -911.8133 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(year) 8.577875 8.950003 332.6079 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = -0.000687 Deviance explained = 0.525%
#> -REML = -1.2164e+05 Scale est. = 1 n = 62762Code
maper_mpepr_gam_4 |>
summarise_r2(
dplyr::mutate(data, year = as.integer(as.character(year))) |>
nrow()
) |>
md_named_tibble()maper_mpepr_gam_4 model.
| Value | Interpretation | Rule | |
|---|---|---|---|
| R2 | 0 | no effect | cohen1988 |
| SE | 0 | NA | NA |
| Lower CI | 0 | no effect | cohen1988 |
| Upper CI | 0 | no effect | cohen1988 |
Source: Created by the authors.
Code
maper_mpepr_gam_4 |>
broom::glance() |>
tidyr::pivot_longer(dplyr::everything()) |>
md_named_tibble()maper_mpepr_gam_4 model.
| Value | |
|---|---|
| df | 9.5778747519 |
| logLik | 121672.7902501706 |
| AIC | -243323.6804947727 |
| BIC | -243224.6146690252 |
| deviance | 64882.8996527854 |
| df.residual | 62752.4221252481 |
| nobs | 62762.0000000000 |
| adj.r.squared | -0.0006872297 |
| npar | 10.0000000000 |
Source: Created by the authors.
Code
maper_mpepr_gam_4 |>
summarise_coefs() |>
md_named_tibble()maper_mpepr_gam_4 model.
| Value | |
|---|---|
| [Mean] | -0.2723942217 |
| (Intercept) | -2.8770190360 |
| mean(s(year)) | 0.0170085354 |
Source: Created by the authors.
Code
maper_mpepr_gam_4 |> mgcViz::getViz() |> mgcViz::check.gamViz()
#>
#> Method: REML Optimizer: outer newton
#> full convergence after 6 iterations.
#> Gradient range [0.001452357338,0.001462095772]
#> (score -121642.3846 & scale 1).
#> Hessian positive definite, eigenvalue range [3.300163003,26958.96005].
#> Model rank = 10 / 10
#>
#> Basis dimension (k) checking results. Low p-value (k-index<1) may
#> indicate that k is too low, especially if edf is close to k'.
#>
#> k' edf k-index p-value
#> s(year) 9.00 8.58 1 0.6
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.Code
dplyr::mutate(data, year = as.integer(as.character(year))) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam(
model = maper_mpepr_gam_4,
type = 4,
x_label = "Years",
y_label = "Predicted probability of MAPER & MPEPR"
)maper_mpepr_gam_4 model. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
By year (Ordered)
In this model, the year variable is treated as a ordered categorical variable.
.L, .Q, and .C are, respectively, the coefficients for the ordered factor coded with linear, quadratic, and cubic contrasts.
mbepr_gam_5 |> summary()
#>
#> Family: Beta regression(17.638)
#> Link function: logit
#>
#> Formula:
#> mbepr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.819724761 0.003245311 -868.86131 < 2.22e-16 ***
#> year.L 0.039878128 0.011320870 3.52253 0.00042745 ***
#> year.Q -0.106048138 0.011379691 -9.31907 < 2.22e-16 ***
#> year.C 0.004592172 0.011329411 0.40533 0.68523353
#> year^4 -0.084506343 0.011264853 -7.50177 0.000000000000062962 ***
#> year^5 0.115842989 0.011244823 10.30190 < 2.22e-16 ***
#> year^6 -0.049357350 0.011184889 -4.41286 0.000010201391317061 ***
#> year^7 -0.009601510 0.011183504 -0.85854 0.39059315
#> year^8 0.052923709 0.011165129 4.74009 0.000002136239494897 ***
#> year^9 -0.019333845 0.011154098 -1.73334 0.08303524 .
#> year^10 -0.058854569 0.011214557 -5.24805 0.000000153716732986 ***
#> year^11 -0.017281456 0.011218670 -1.54042 0.12345819
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = -0.00327 Deviance explained = 0.525%
#> -REML = -1.1795e+05 Scale est. = 1 n = 62762Code
mbepr_gam_5 |>
summarise_r2(
data |>
nrow()
) |>
md_named_tibble()mbepr_gam_5 model.
| Value | Interpretation | Rule | |
|---|---|---|---|
| R2 | 0 | no effect | cohen1988 |
| SE | 0 | NA | NA |
| Lower CI | 0 | no effect | cohen1988 |
| Upper CI | 0 | no effect | cohen1988 |
Source: Created by the authors.
Code
mbepr_gam_5 |>
broom::glance() |>
tidyr::pivot_longer(dplyr::everything()) |>
md_named_tibble()mbepr_gam_5 model.
| Value | |
|---|---|
| df | 12.0000000000 |
| logLik | 117994.6877479883 |
| AIC | -235963.3754959765 |
| BIC | -235845.7631300175 |
| deviance | 64485.5210188838 |
| df.residual | 62750.0000000000 |
| nobs | 62762.0000000000 |
| adj.r.squared | -0.0032733397 |
| npar | 12.0000000000 |
Source: Created by the authors.
Code
mbepr_gam_5 |>
summarise_coefs() |>
md_named_tibble()mbepr_gam_5 model.
| Value | |
|---|---|
| [Mean] | -0.2459559144 |
| (Intercept) | -2.8197247609 |
| year.L | 0.0398781283 |
| year.Q | -0.1060481384 |
| year.C | 0.0045921722 |
| year^4 | -0.0845063430 |
| year^5 | 0.1158429895 |
| year^6 | -0.0493573500 |
| year^7 | -0.0096015103 |
| year^8 | 0.0529237091 |
| year^9 | -0.0193338448 |
| year^10 | -0.0588545690 |
| year^11 | -0.0172814558 |
Source: Created by the authors.
Code
mbepr_gam_5 |> mgcViz::getViz() |> mgcViz::check.gamViz()
#>
#> Method: REML Optimizer: outer newton
#> full convergence after 5 iterations.
#> Gradient range [0.000001198946155,0.000001198946155]
#> (score -117950.6115 & scale 1).
#> Hessian positive definite, eigenvalue range [26571.0456,26571.0456].
#> Model rank = 12 / 12
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.Code
data |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam(
model = mbepr_gam_5,
type = 5,
x_label = "Years",
y_label = "Predicted probability of MBEPR"
)mbepr_gam_5 model. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
beipr_gam_5 |> summary()
#>
#> Family: Beta regression(25.798)
#> Link function: logit
#>
#> Formula:
#> beipr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.649018998 0.002748798 -963.70086 < 2.22e-16 ***
#> year.L 0.089565087 0.009525353 9.40281 < 2.22e-16 ***
#> year.Q 0.008970089 0.009602439 0.93415 0.3502281
#> year.C -0.026710792 0.009568146 -2.79164 0.0052442 **
#> year^4 -0.070578182 0.009512419 -7.41958 0.00000000000011749 ***
#> year^5 0.082998344 0.009501906 8.73492 < 2.22e-16 ***
#> year^6 -0.043857480 0.009483389 -4.62466 0.00000375207630563 ***
#> year^7 -0.043134260 0.009459485 -4.55990 0.00000511791590338 ***
#> year^8 0.048173854 0.009463350 5.09057 0.00000035698739739 ***
#> year^9 0.004749118 0.009500885 0.49986 0.6171732
#> year^10 -0.003885200 0.009548341 -0.40690 0.6840830
#> year^11 0.047418864 0.009576401 4.95164 0.00000073591609239 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = -0.00784 Deviance explained = 0.52%
#> -REML = -1.1332e+05 Scale est. = 1 n = 62762Code
beipr_gam_5 |>
summarise_r2(
data |>
nrow()
) |>
md_named_tibble()beipr_gam_5 model.
| Value | Interpretation | Rule | |
|---|---|---|---|
| R2 | 0 | no effect | cohen1988 |
| SE | 0 | NA | NA |
| Lower CI | 0 | no effect | cohen1988 |
| Upper CI | 0 | no effect | cohen1988 |
Source: Created by the authors.
Code
beipr_gam_5 |>
broom::glance() |>
tidyr::pivot_longer(dplyr::everything()) |>
md_named_tibble()beipr_gam_5 model.
| Value | |
|---|---|
| df | 12.0000000000 |
| logLik | 113362.5968849334 |
| AIC | -226699.1937698668 |
| BIC | -226581.5814039078 |
| deviance | 63831.4178238831 |
| df.residual | 62750.0000000000 |
| nobs | 62762.0000000000 |
| adj.r.squared | -0.0078397415 |
| npar | 12.0000000000 |
Source: Created by the authors.
Code
beipr_gam_5 |>
summarise_coefs() |>
md_named_tibble()beipr_gam_5 model.
| Value | |
|---|---|
| [Mean] | -0.2129424629 |
| (Intercept) | -2.6490189976 |
| year.L | 0.0895650875 |
| year.Q | 0.0089700894 |
| year.C | -0.0267107916 |
| year^4 | -0.0705781816 |
| year^5 | 0.0829983439 |
| year^6 | -0.0438574801 |
| year^7 | -0.0431342600 |
| year^8 | 0.0481738541 |
| year^9 | 0.0047491179 |
| year^10 | -0.0038852003 |
| year^11 | 0.0474188640 |
Source: Created by the authors.
Code
beipr_gam_5 |> mgcViz::getViz() |> mgcViz::check.gamViz()
#>
#> Method: REML Optimizer: outer newton
#> full convergence after 5 iterations.
#> Gradient range [0.00000875780144,0.00000875780144]
#> (score -113316.5276 & scale 1).
#> Hessian positive definite, eigenvalue range [29161.5517,29161.5517].
#> Model rank = 12 / 12
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.Code
data |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam(
model = beipr_gam_5,
type = 5,
x_label = "Years",
y_label = "Predicted probability of BEIPR"
)beipr_gam_5 model. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
mbepr_beipr_gam_5 |> summary()
#>
#> Family: Beta regression(16.296)
#> Link function: logit
#>
#> Formula:
#> mbepr_beipr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -1.965102548 0.002685499 -731.74585 < 2.22e-16 ***
#> year.L -0.047271406 0.009320041 -5.07202 0.00000039362084 ***
#> year.Q -0.013637154 0.009377919 -1.45418 0.14589726
#> year.C -0.007039030 0.009352037 -0.75267 0.45164616
#> year^4 -0.058196732 0.009300741 -6.25721 0.00000000039191 ***
#> year^5 0.093573558 0.009290835 10.07160 < 2.22e-16 ***
#> year^6 -0.052789757 0.009257180 -5.70257 0.00000001180112 ***
#> year^7 -0.020548391 0.009258158 -2.21949 0.02645340 *
#> year^8 0.046041585 0.009257142 4.97363 0.00000065711276 ***
#> year^9 0.005464968 0.009268416 0.58963 0.55543643
#> year^10 -0.035902530 0.009320676 -3.85192 0.00011719 ***
#> year^11 0.012717049 0.009327199 1.36344 0.17274482
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = 0.00446 Deviance explained = 0.406%
#> -REML = -78439 Scale est. = 1 n = 62762Code
mbepr_beipr_gam_5 |>
summarise_r2(
data |>
nrow()
) |>
md_named_tibble()mbepr_beipr_gam_5 model.
| Value | Interpretation | Rule | |
|---|---|---|---|
| R2 | 0.0044644574 | very weak (negligible) | cohen1988 |
| SE | 0.0005310049 | NA | NA |
| Lower CI | 0.0034237070 | very weak (negligible) | cohen1988 |
| Upper CI | 0.0055052078 | very weak (negligible) | cohen1988 |
Source: Created by the authors.
Code
mbepr_beipr_gam_5 |>
broom::glance() |>
tidyr::pivot_longer(dplyr::everything()) |>
md_named_tibble()mbepr_beipr_gam_5 model.
| Value | |
|---|---|
| df | 12.0000000000 |
| logLik | 78485.5946634256 |
| AIC | -156945.1893268511 |
| BIC | -156827.5769608921 |
| deviance | 61789.7893367158 |
| df.residual | 62750.0000000000 |
| nobs | 62762.0000000000 |
| adj.r.squared | 0.0044644574 |
| npar | 12.0000000000 |
Source: Created by the authors.
Code
mbepr_beipr_gam_5 |>
summarise_coefs() |>
md_named_tibble()mbepr_beipr_gam_5 model.
| Value | |
|---|---|
| [Mean] | -0.1702241990 |
| (Intercept) | -1.9651025476 |
| year.L | -0.0472714062 |
| year.Q | -0.0136371535 |
| year.C | -0.0070390298 |
| year^4 | -0.0581967323 |
| year^5 | 0.0935735582 |
| year^6 | -0.0527897574 |
| year^7 | -0.0205483915 |
| year^8 | 0.0460415848 |
| year^9 | 0.0054649678 |
| year^10 | -0.0359025295 |
| year^11 | 0.0127170490 |
Source: Created by the authors.
Code
mbepr_beipr_gam_5 |> mgcViz::getViz() |> mgcViz::check.gamViz()
#>
#> Method: REML Optimizer: outer newton
#> full convergence after 5 iterations.
#> Gradient range [0.01219855648,0.01219855648]
#> (score -78439.24791 & scale 1).
#> Hessian positive definite, eigenvalue range [30826.9659,30826.9659].
#> Model rank = 12 / 12
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.Code
data |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam(
model = mbepr_beipr_gam_5,
type = 5,
x_label = "Years",
y_label = "Predicted probability of MBEPR & BEIPR"
)mbepr_beipr_gam_5 model. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
maper_gam_5 |> summary()
#>
#> Family: Beta regression(24.482)
#> Link function: logit
#>
#> Formula:
#> maper ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.671007620 0.003548104 -1034.63917 < 2.22e-16 ***
#> year.L 0.027842144 0.012368692 2.25102 0.0243844 *
#> year.Q -0.134341841 0.012419112 -10.81735 < 2.22e-16 ***
#> year.C -0.082483360 0.012340935 -6.68372 0.000000000023295072 ***
#> year^4 -0.080548801 0.012313726 -6.54138 0.000000000060952495 ***
#> year^5 0.079273119 0.012318076 6.43551 0.000000000123058147 ***
#> year^6 0.024429920 0.012282057 1.98907 0.0466930 *
#> year^7 0.035558528 0.012236630 2.90591 0.0036619 **
#> year^8 0.092660310 0.012200680 7.59468 0.000000000000030854 ***
#> year^9 -0.006557267 0.012197699 -0.53758 0.5908655
#> year^10 -0.025618488 0.012238256 -2.09331 0.0363213 *
#> year^11 0.011818501 0.012283076 0.96218 0.3359604
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = -0.00149 Deviance explained = 0.495%
#> -REML = -1.752e+05 Scale est. = 1 n = 62762Code
maper_gam_5 |>
summarise_r2(
data |>
nrow()
) |>
md_named_tibble()maper_gam_5 model.
| Value | Interpretation | Rule | |
|---|---|---|---|
| R2 | 0 | no effect | cohen1988 |
| SE | 0 | NA | NA |
| Lower CI | 0 | no effect | cohen1988 |
| Upper CI | 0 | no effect | cohen1988 |
Source: Created by the authors.
Code
maper_gam_5 |>
broom::glance() |>
tidyr::pivot_longer(dplyr::everything()) |>
md_named_tibble()maper_gam_5 model.
| Value | |
|---|---|
| df | 12.0000000000 |
| logLik | 175246.8729737456 |
| AIC | -350467.7459474911 |
| BIC | -350350.1335815321 |
| deviance | 67168.5892269482 |
| df.residual | 62750.0000000000 |
| nobs | 62762.0000000000 |
| adj.r.squared | -0.0014912039 |
| npar | 12.0000000000 |
Source: Created by the authors.
Code
maper_gam_5 |>
summarise_coefs() |>
md_named_tibble()maper_gam_5 model.
| Value | |
|---|---|
| [Mean] | -0.3107479047 |
| (Intercept) | -3.6710076200 |
| year.L | 0.0278421438 |
| year.Q | -0.1343418412 |
| year.C | -0.0824833604 |
| year^4 | -0.0805488010 |
| year^5 | 0.0792731188 |
| year^6 | 0.0244299196 |
| year^7 | 0.0355585277 |
| year^8 | 0.0926603095 |
| year^9 | -0.0065572665 |
| year^10 | -0.0256184884 |
| year^11 | 0.0118185012 |
Source: Created by the authors.
Code
maper_gam_5 |> mgcViz::getViz() |> mgcViz::check.gamViz()
#>
#> Method: REML Optimizer: outer newton
#> full convergence after 4 iterations.
#> Gradient range [0.0000105819692,0.0000105819692]
#> (score -175203.8687 & scale 1).
#> Hessian positive definite, eigenvalue range [21654.98712,21654.98712].
#> Model rank = 12 / 12
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.Code
data |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam(
model = maper_gam_5,
type = 5,
x_label = "Years",
y_label = "Predicted probability of MAPER"
)maper_gam_5 model. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
mpepr_gam_5 |> summary()
#>
#> Family: Beta regression(30.606)
#> Link function: logit
#>
#> Formula:
#> mpepr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.531198908 0.003292509 -1072.49476 < 2.22e-16 ***
#> year.L 0.153669624 0.011448326 13.42289 < 2.22e-16 ***
#> year.Q -0.049777612 0.011560586 -4.30580 0.000016638072 ***
#> year.C -0.061042356 0.011439084 -5.33630 0.000000094864 ***
#> year^4 -0.152562348 0.011424506 -13.35396 < 2.22e-16 ***
#> year^5 0.023769084 0.011408711 2.08342 0.0372134 *
#> year^6 0.053608763 0.011388065 4.70745 0.000002508330 ***
#> year^7 0.032808996 0.011321353 2.89797 0.0037558 **
#> year^8 0.051603530 0.011292849 4.56958 0.000004887127 ***
#> year^9 -0.007970576 0.011315547 -0.70439 0.4811890
#> year^10 0.012958743 0.011360197 1.14071 0.2539887
#> year^11 0.021167522 0.011499317 1.84076 0.0656562 .
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = -0.0125 Deviance explained = 0.712%
#> -REML = -1.6102e+05 Scale est. = 1 n = 62762Code
mpepr_gam_5 |>
summarise_r2(
data |>
nrow()
) |>
md_named_tibble()mpepr_gam_5 model.
| Value | Interpretation | Rule | |
|---|---|---|---|
| R2 | 0 | no effect | cohen1988 |
| SE | 0 | NA | NA |
| Lower CI | 0 | no effect | cohen1988 |
| Upper CI | 0 | no effect | cohen1988 |
Source: Created by the authors.
Code
mpepr_gam_5 |>
broom::glance() |>
tidyr::pivot_longer(dplyr::everything()) |>
md_named_tibble()mpepr_gam_5 model.
| Value | |
|---|---|
| df | 12.0000000000 |
| logLik | 161065.5110249491 |
| AIC | -322105.0220498982 |
| BIC | -321987.4096839392 |
| deviance | 67283.6524796425 |
| df.residual | 62750.0000000000 |
| nobs | 62762.0000000000 |
| adj.r.squared | -0.0125163328 |
| npar | 12.0000000000 |
Source: Created by the authors.
Code
mpepr_gam_5 |>
summarise_coefs() |>
md_named_tibble()mpepr_gam_5 model.
| Value | |
|---|---|
| [Mean] | -0.2877471282 |
| (Intercept) | -3.5311989080 |
| year.L | 0.1536696243 |
| year.Q | -0.0497776119 |
| year.C | -0.0610423562 |
| year^4 | -0.1525623482 |
| year^5 | 0.0237690842 |
| year^6 | 0.0536087631 |
| year^7 | 0.0328089956 |
| year^8 | 0.0516035296 |
| year^9 | -0.0079705756 |
| year^10 | 0.0129587426 |
| year^11 | 0.0211675220 |
Source: Created by the authors.
Code
mpepr_gam_5 |> mgcViz::getViz() |> mgcViz::check.gamViz()
#>
#> Method: REML Optimizer: outer newton
#> full convergence after 3 iterations.
#> Gradient range [0.06495643988,0.06495643988]
#> (score -161021.6064 & scale 1).
#> Hessian positive definite, eigenvalue range [24663.52749,24663.52749].
#> Model rank = 12 / 12
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.Code
data |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam(
model = mpepr_gam_5,
type = 5,
x_label = "Years",
y_label = "Predicted probability of MPEPR"
)mpepr_gam_5 model. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
maper_mpepr_gam_5 |> summary()
#>
#> Family: Beta regression(20.406)
#> Link function: logit
#>
#> Formula:
#> maper_mpepr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.877375499 0.003155866 -911.75453 < 2.22e-16 ***
#> year.L 0.013586860 0.010994060 1.23584 0.21652
#> year.Q -0.078213051 0.011085949 -7.05515 0.0000000000017241 ***
#> year.C -0.070927872 0.010973416 -6.46361 0.0000000001022349 ***
#> year^4 -0.128530430 0.010948898 -11.73912 < 2.22e-16 ***
#> year^5 0.046957484 0.010954014 4.28678 0.0000181278821559 ***
#> year^6 0.047973032 0.010925669 4.39086 0.0000112905702940 ***
#> year^7 0.056102588 0.010852567 5.16952 0.0000002346931480 ***
#> year^8 0.076581290 0.010814002 7.08168 0.0000000000014242 ***
#> year^9 -0.008376653 0.010832943 -0.77326 0.43937
#> year^10 0.006769788 0.010884854 0.62195 0.53398
#> year^11 0.004430077 0.010985307 0.40327 0.68675
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = -0.000592 Deviance explained = 0.552%
#> -REML = -1.2164e+05 Scale est. = 1 n = 62762Code
maper_mpepr_gam_5 |>
summarise_r2(
data |>
nrow()
) |>
md_named_tibble()maper_mpepr_gam_5 model.
| Value | Interpretation | Rule | |
|---|---|---|---|
| R2 | 0 | no effect | cohen1988 |
| SE | 0 | NA | NA |
| Lower CI | 0 | no effect | cohen1988 |
| Upper CI | 0 | no effect | cohen1988 |
Source: Created by the authors.
Code
maper_mpepr_gam_5 |>
broom::glance() |>
tidyr::pivot_longer(dplyr::everything()) |>
md_named_tibble()maper_mpepr_gam_5 model.
| Value | |
|---|---|
| df | 12.0000000000 |
| logLik | 121681.2905335238 |
| AIC | -243336.5810670477 |
| BIC | -243218.9687010887 |
| deviance | 64886.5484799453 |
| df.residual | 62750.0000000000 |
| nobs | 62762.0000000000 |
| adj.r.squared | -0.0005918146 |
| npar | 12.0000000000 |
Source: Created by the authors.
Code
maper_mpepr_gam_5 |>
summarise_coefs() |>
md_named_tibble()maper_mpepr_gam_5 model.
| Value | |
|---|---|
| [Mean] | -0.2425851988 |
| (Intercept) | -2.8773754994 |
| year.L | 0.0135868602 |
| year.Q | -0.0782130509 |
| year.C | -0.0709278716 |
| year^4 | -0.1285304305 |
| year^5 | 0.0469574842 |
| year^6 | 0.0479730318 |
| year^7 | 0.0561025880 |
| year^8 | 0.0765812902 |
| year^9 | -0.0083766531 |
| year^10 | 0.0067697882 |
| year^11 | 0.0044300767 |
Source: Created by the authors.
Code
maper_mpepr_gam_5 |> mgcViz::getViz() |> mgcViz::check.gamViz()
#>
#> Method: REML Optimizer: outer newton
#> full convergence after 4 iterations.
#> Gradient range [0.1322078474,0.1322078474]
#> (score -121636.8789 & scale 1).
#> Hessian positive definite, eigenvalue range [26961.29141,26961.29141].
#> Model rank = 12 / 12
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.Code
data |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam(
model = maper_mpepr_gam_5,
type = 5,
x_label = "Years",
y_label = "Predicted probability of MAPER & MPEPR"
)maper_mpepr_gam_5 model. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
By year (Unordered)
In this model, the year variable is treated as a unordered categorical variable.
mbepr_gam_6 |> summary()
#>
#> Family: Beta regression(17.638)
#> Link function: logit
#>
#> Formula:
#> mbepr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.95978829 0.01184997 -249.77179 < 2.22e-16 ***
#> year2009 0.18581894 0.01623717 11.44404 < 2.22e-16 ***
#> year2010 0.19650008 0.01620364 12.12691 < 2.22e-16 ***
#> year2011 0.11636277 0.01634690 7.11834 0.000000000001092351 ***
#> year2012 0.07206778 0.01640557 4.39288 0.000011185640406729 ***
#> year2013 0.16526735 0.01635417 10.10552 < 2.22e-16 ***
#> year2014 0.21516820 0.01625094 13.24035 < 2.22e-16 ***
#> year2015 0.14714754 0.01632144 9.01560 < 2.22e-16 ***
#> year2016 0.20560208 0.01618365 12.70431 < 2.22e-16 ***
#> year2017 0.15465732 0.01628361 9.49773 < 2.22e-16 ***
#> year2018 0.12309673 0.01633175 7.53727 0.000000000000047993 ***
#> year2019 0.09907351 0.01632576 6.06854 0.000000001290783738 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = -0.00327 Deviance explained = 0.525%
#> -REML = -1.1795e+05 Scale est. = 1 n = 62762Code
mbepr_gam_6 model.
| Value | Interpretation | Rule | |
|---|---|---|---|
| R2 | 0 | no effect | cohen1988 |
| SE | 0 | NA | NA |
| Lower CI | 0 | no effect | cohen1988 |
| Upper CI | 0 | no effect | cohen1988 |
Source: Created by the authors.
Code
mbepr_gam_6 |>
broom::glance() |>
tidyr::pivot_longer(dplyr::everything()) |>
md_named_tibble()mbepr_gam_6 model.
| Value | |
|---|---|
| df | 12.0000000000 |
| logLik | 117994.6877479886 |
| AIC | -235963.3754959772 |
| BIC | -235845.7631300182 |
| deviance | 64485.5210188823 |
| df.residual | 62750.0000000000 |
| nobs | 62762.0000000000 |
| adj.r.squared | -0.0032733397 |
| npar | 12.0000000000 |
Source: Created by the authors.
Code
mbepr_gam_6 |>
summarise_coefs() |>
md_named_tibble()mbepr_gam_6 model.
| Value | |
|---|---|
| [Mean] | -0.1065854982 |
| (Intercept) | -2.9597882866 |
| year2009 | 0.1858189412 |
| year2010 | 0.1965000821 |
| year2011 | 0.1163627678 |
| year2012 | 0.0720677836 |
| year2013 | 0.1652673488 |
| year2014 | 0.2151681982 |
| year2015 | 0.1471475383 |
| year2016 | 0.2056020840 |
| year2017 | 0.1546573211 |
| year2018 | 0.1230967302 |
| year2019 | 0.0990735131 |
Source: Created by the authors.
Code
mbepr_gam_6 |> mgcViz::getViz() |> mgcViz::check.gamViz()
#>
#> Method: REML Optimizer: outer newton
#> full convergence after 5 iterations.
#> Gradient range [0.00000119875011,0.00000119875011]
#> (score -117951.854 & scale 1).
#> Hessian positive definite, eigenvalue range [26571.0456,26571.0456].
#> Model rank = 12 / 12
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.Code
dplyr::mutate(data, year = factor(year, ordered = FALSE)) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam(
model = mbepr_gam_6,
type = 6,
x_label = "Years",
y_label = "Predicted probability of MBEPR"
)mbepr_gam_6 model. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
beipr_gam_6 |> summary()
#>
#> Family: Beta regression(25.798)
#> Link function: logit
#>
#> Formula:
#> beipr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.722549043 0.009951744 -273.57506 < 2.22e-16 ***
#> year2009 0.093774149 0.013717615 6.83604 8.1413e-12 ***
#> year2010 0.106949012 0.013679330 7.81829 5.3544e-15 ***
#> year2011 0.025696817 0.013841904 1.85645 0.063389 .
#> year2012 -0.037917921 0.013952806 -2.71758 0.006576 **
#> year2013 0.070849601 0.013832071 5.12213 3.0211e-07 ***
#> year2014 0.080692900 0.013799146 5.84767 4.9850e-09 ***
#> year2015 0.124328975 0.013673487 9.09270 < 2.22e-16 ***
#> year2016 0.085008464 0.013717882 6.19691 5.7583e-10 ***
#> year2017 0.121341258 0.013658424 8.88399 < 2.22e-16 ***
#> year2018 0.117922729 0.013660107 8.63264 < 2.22e-16 ***
#> year2019 0.093714562 0.013667701 6.85664 7.0497e-12 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = -0.00784 Deviance explained = 0.52%
#> -REML = -1.1332e+05 Scale est. = 1 n = 62762Code
beipr_gam_6 model.
| Value | Interpretation | Rule | |
|---|---|---|---|
| R2 | 0 | no effect | cohen1988 |
| SE | 0 | NA | NA |
| Lower CI | 0 | no effect | cohen1988 |
| Upper CI | 0 | no effect | cohen1988 |
Source: Created by the authors.
Code
beipr_gam_6 |>
broom::glance() |>
tidyr::pivot_longer(dplyr::everything()) |>
md_named_tibble()beipr_gam_6 model.
| Value | |
|---|---|
| df | 12.0000000000 |
| logLik | 113362.5968849338 |
| AIC | -226699.1937698676 |
| BIC | -226581.5814039086 |
| deviance | 63831.4178238829 |
| df.residual | 62750.0000000000 |
| nobs | 62762.0000000000 |
| adj.r.squared | -0.0078397415 |
| npar | 12.0000000000 |
Source: Created by the authors.
Code
beipr_gam_6 |>
summarise_coefs() |>
md_named_tibble()beipr_gam_6 model.
| Value | |
|---|---|
| [Mean] | -0.1533490415 |
| (Intercept) | -2.7225490430 |
| year2009 | 0.0937741492 |
| year2010 | 0.1069490117 |
| year2011 | 0.0256968171 |
| year2012 | -0.0379179214 |
| year2013 | 0.0708496009 |
| year2014 | 0.0806929002 |
| year2015 | 0.1243289749 |
| year2016 | 0.0850084637 |
| year2017 | 0.1213412578 |
| year2018 | 0.1179227286 |
| year2019 | 0.0937145617 |
Source: Created by the authors.
Code
beipr_gam_6 |> mgcViz::getViz() |> mgcViz::check.gamViz()
#>
#> Method: REML Optimizer: outer newton
#> full convergence after 5 iterations.
#> Gradient range [0.000008758086041,0.000008758086041]
#> (score -113317.7701 & scale 1).
#> Hessian positive definite, eigenvalue range [29161.5517,29161.5517].
#> Model rank = 12 / 12
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.Code
dplyr::mutate(data, year = factor(year, ordered = FALSE)) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam(
model = beipr_gam_6,
type = 6,
x_label = "Years",
y_label = "Predicted probability of BEIPR"
)beipr_gam_6 model. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
mbepr_beipr_gam_6 |> summary()
#>
#> Family: Beta regression(16.296)
#> Link function: logit
#>
#> Formula:
#> mbepr_beipr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -1.998038053 0.009599818 -208.13291 < 2.22e-16 ***
#> year2009 0.115589875 0.013212260 8.74868 < 2.22e-16 ***
#> year2010 0.093268110 0.013236994 7.04602 0.0000000000018411 ***
#> year2011 0.020589852 0.013365365 1.54054 0.12342928
#> year2012 -0.046723027 0.013469180 -3.46888 0.00052262 ***
#> year2013 0.042609937 0.013403990 3.17890 0.00147835 **
#> year2014 0.068768866 0.013345526 5.15295 0.0000002564166243 ***
#> year2015 0.035954417 0.013361657 2.69087 0.00712670 **
#> year2016 0.032964579 0.013335521 2.47194 0.01343829 *
#> year2017 0.027139886 0.013355914 2.03205 0.04214858 *
#> year2018 0.009562646 0.013381355 0.71462 0.47484103
#> year2019 -0.004499079 0.013366541 -0.33659 0.73642405
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = 0.00446 Deviance explained = 0.406%
#> -REML = -78440 Scale est. = 1 n = 62762Code
mbepr_beipr_gam_6 model.
| Value | Interpretation | Rule | |
|---|---|---|---|
| R2 | 0.0044644574 | very weak (negligible) | cohen1988 |
| SE | 0.0005310049 | NA | NA |
| Lower CI | 0.0034237070 | very weak (negligible) | cohen1988 |
| Upper CI | 0.0055052078 | very weak (negligible) | cohen1988 |
Source: Created by the authors.
Code
mbepr_beipr_gam_6 |>
broom::glance() |>
tidyr::pivot_longer(dplyr::everything()) |>
md_named_tibble()mbepr_beipr_gam_6 model.
| Value | |
|---|---|
| df | 12.0000000000 |
| logLik | 78485.5946634255 |
| AIC | -156945.1893268510 |
| BIC | -156827.5769608920 |
| deviance | 61789.7893367161 |
| df.residual | 62750.0000000000 |
| nobs | 62762.0000000000 |
| adj.r.squared | 0.0044644574 |
| npar | 12.0000000000 |
Source: Created by the authors.
Code
mbepr_beipr_gam_6 |>
summarise_coefs() |>
md_named_tibble()mbepr_beipr_gam_6 model.
| Value | |
|---|---|
| [Mean] | -0.1335676658 |
| (Intercept) | -1.9980380529 |
| year2009 | 0.1155898751 |
| year2010 | 0.0932681104 |
| year2011 | 0.0205898519 |
| year2012 | -0.0467230271 |
| year2013 | 0.0426099372 |
| year2014 | 0.0687688662 |
| year2015 | 0.0359544170 |
| year2016 | 0.0329645792 |
| year2017 | 0.0271398862 |
| year2018 | 0.0095626455 |
| year2019 | -0.0044990787 |
Source: Created by the authors.
Code
mbepr_beipr_gam_6 |> mgcViz::getViz() |> mgcViz::check.gamViz()
#>
#> Method: REML Optimizer: outer newton
#> full convergence after 5 iterations.
#> Gradient range [0.01219855661,0.01219855661]
#> (score -78440.49037 & scale 1).
#> Hessian positive definite, eigenvalue range [30826.9659,30826.9659].
#> Model rank = 12 / 12
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.Code
dplyr::mutate(data, year = factor(year, ordered = FALSE)) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam(
model = mbepr_beipr_gam_6,
type = 6,
x_label = "Years",
y_label = "Predicted probability of MBEPR & BEIPR"
)mbepr_beipr_gam_6 model. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
maper_gam_6 |> summary()
#>
#> Family: Beta regression(24.482)
#> Link function: logit
#>
#> Formula:
#> maper ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.758990530 0.012747837 -294.87282 < 2.22e-16 ***
#> year2009 0.083861654 0.017695514 4.73915 0.000002146191308382 ***
#> year2010 0.126540065 0.017619775 7.18171 0.000000000000688463 ***
#> year2011 0.058108129 0.017719687 3.27930 0.0010407 **
#> year2012 0.030105437 0.017738763 1.69716 0.0896673 .
#> year2013 0.124723975 0.017728977 7.03504 0.000000000001992108 ***
#> year2014 0.134593862 0.017697517 7.60524 0.000000000000028438 ***
#> year2015 0.119405131 0.017665879 6.75908 0.000000000013886856 ***
#> year2016 0.174963896 0.017546352 9.97153 < 2.22e-16 ***
#> year2017 0.190981494 0.017536505 10.89051 < 2.22e-16 ***
#> year2018 0.015059851 0.017772131 0.84739 0.3967802
#> year2019 -0.002548577 0.017742683 -0.14364 0.8857840
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = -0.00149 Deviance explained = 0.495%
#> -REML = -1.7521e+05 Scale est. = 1 n = 62762Code
maper_gam_6 model.
| Value | Interpretation | Rule | |
|---|---|---|---|
| R2 | 0 | no effect | cohen1988 |
| SE | 0 | NA | NA |
| Lower CI | 0 | no effect | cohen1988 |
| Upper CI | 0 | no effect | cohen1988 |
Source: Created by the authors.
Code
maper_gam_6 |>
broom::glance() |>
tidyr::pivot_longer(dplyr::everything()) |>
md_named_tibble()maper_gam_6 model.
| Value | |
|---|---|
| df | 12.0000000000 |
| logLik | 175246.8729737457 |
| AIC | -350467.7459474914 |
| BIC | -350350.1335815324 |
| deviance | 67168.5892269479 |
| df.residual | 62750.0000000000 |
| nobs | 62762.0000000000 |
| adj.r.squared | -0.0014912039 |
| npar | 12.0000000000 |
Source: Created by the authors.
Code
maper_gam_6 |>
summarise_coefs() |>
md_named_tibble()maper_gam_6 model.
| Value | |
|---|---|
| [Mean] | -0.2252663011 |
| (Intercept) | -3.7589905297 |
| year2009 | 0.0838616542 |
| year2010 | 0.1265400648 |
| year2011 | 0.0581081288 |
| year2012 | 0.0301054374 |
| year2013 | 0.1247239748 |
| year2014 | 0.1345938625 |
| year2015 | 0.1194051310 |
| year2016 | 0.1749638956 |
| year2017 | 0.1909814936 |
| year2018 | 0.0150598506 |
| year2019 | -0.0025485765 |
Source: Created by the authors.
Code
maper_gam_6 |> mgcViz::getViz() |> mgcViz::check.gamViz()
#>
#> Method: REML Optimizer: outer newton
#> full convergence after 4 iterations.
#> Gradient range [0.00001058207839,0.00001058207839]
#> (score -175205.1112 & scale 1).
#> Hessian positive definite, eigenvalue range [21654.98712,21654.98712].
#> Model rank = 12 / 12
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.Code
dplyr::mutate(data, year = factor(year, ordered = FALSE)) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam(
model = maper_gam_6,
type = 6,
x_label = "Years",
y_label = "Predicted probability of MAPER"
)maper_gam_6 model. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
mpepr_gam_6 |> summary()
#>
#> Family: Beta regression(30.606)
#> Link function: logit
#>
#> Formula:
#> mpepr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.65301970 0.01197372 -305.08648 < 2.22e-16 ***
#> year2009 0.08052386 0.01658941 4.85393 0.00000121037627 ***
#> year2010 0.14196333 0.01646757 8.62078 < 2.22e-16 ***
#> year2011 0.09031173 0.01656285 5.45267 0.00000004961916 ***
#> year2012 0.06937855 0.01658203 4.18396 0.00002864737535 ***
#> year2013 0.09082284 0.01665623 5.45278 0.00000004958750 ***
#> year2014 0.07948343 0.01665956 4.77104 0.00000183275897 ***
#> year2015 0.14890933 0.01648873 9.03098 < 2.22e-16 ***
#> year2016 0.21623256 0.01633233 13.23954 < 2.22e-16 ***
#> year2017 0.28393957 0.01622278 17.50252 < 2.22e-16 ***
#> year2018 0.15693014 0.01644361 9.54353 < 2.22e-16 ***
#> year2019 0.10335415 0.01648944 6.26790 0.00000000036595 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = -0.0125 Deviance explained = 0.712%
#> -REML = -1.6102e+05 Scale est. = 1 n = 62762Code
mpepr_gam_6 model.
| Value | Interpretation | Rule | |
|---|---|---|---|
| R2 | 0 | no effect | cohen1988 |
| SE | 0 | NA | NA |
| Lower CI | 0 | no effect | cohen1988 |
| Upper CI | 0 | no effect | cohen1988 |
Source: Created by the authors.
Code
mpepr_gam_6 |>
broom::glance() |>
tidyr::pivot_longer(dplyr::everything()) |>
md_named_tibble()mpepr_gam_6 model.
| Value | |
|---|---|
| df | 12.0000000000 |
| logLik | 161065.5110249493 |
| AIC | -322105.0220498986 |
| BIC | -321987.4096839396 |
| deviance | 67283.6524796410 |
| df.residual | 62750.0000000000 |
| nobs | 62762.0000000000 |
| adj.r.squared | -0.0125163328 |
| npar | 12.0000000000 |
Source: Created by the authors.
Code
mpepr_gam_6 |>
summarise_coefs() |>
md_named_tibble()mpepr_gam_6 model.
| Value | |
|---|---|
| [Mean] | -0.1825975171 |
| (Intercept) | -3.6530196992 |
| year2009 | 0.0805238602 |
| year2010 | 0.1419633321 |
| year2011 | 0.0903117322 |
| year2012 | 0.0693785534 |
| year2013 | 0.0908228362 |
| year2014 | 0.0794834342 |
| year2015 | 0.1489093298 |
| year2016 | 0.2162325595 |
| year2017 | 0.2839395689 |
| year2018 | 0.1569301378 |
| year2019 | 0.1033541501 |
Source: Created by the authors.
Code
mpepr_gam_6 |> mgcViz::getViz() |> mgcViz::check.gamViz()
#>
#> Method: REML Optimizer: outer newton
#> full convergence after 3 iterations.
#> Gradient range [0.06495643969,0.06495643969]
#> (score -161022.8488 & scale 1).
#> Hessian positive definite, eigenvalue range [24663.52749,24663.52749].
#> Model rank = 12 / 12
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.Code
dplyr::mutate(data, year = factor(year, ordered = FALSE)) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam(
model = mpepr_gam_6,
type = 6,
x_label = "Years",
y_label = "Predicted probability of MPEPR"
)mpepr_gam_6 model. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
maper_mpepr_gam_6 |> summary()
#>
#> Family: Beta regression(20.406)
#> Link function: logit
#>
#> Formula:
#> maper_mpepr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.94365857 0.01135972 -259.13115 < 2.22e-16 ***
#> year2009 0.07932584 0.01572402 5.04488 0.000000453801089922 ***
#> year2010 0.12042580 0.01563447 7.70258 0.000000000000013334 ***
#> year2011 0.04361417 0.01577935 2.76400 0.00570971 **
#> year2012 0.03529717 0.01577849 2.23704 0.02528347 *
#> year2013 0.05934068 0.01584106 3.74601 0.00017967 ***
#> year2014 0.05298592 0.01583706 3.34569 0.00082078 ***
#> year2015 0.07218084 0.01575428 4.58166 0.000004612884552903 ***
#> year2016 0.14183664 0.01559137 9.09713 < 2.22e-16 ***
#> year2017 0.19522378 0.01550575 12.59041 < 2.22e-16 ***
#> year2018 0.01346871 0.01583000 0.85083 0.39486145
#> year2019 -0.01830271 0.01584025 -1.15546 0.24790357
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = -0.000592 Deviance explained = 0.552%
#> -REML = -1.2164e+05 Scale est. = 1 n = 62762Code
maper_mpepr_gam_6 model.
| Value | Interpretation | Rule | |
|---|---|---|---|
| R2 | 0 | no effect | cohen1988 |
| SE | 0 | NA | NA |
| Lower CI | 0 | no effect | cohen1988 |
| Upper CI | 0 | no effect | cohen1988 |
Source: Created by the authors.
Code
maper_mpepr_gam_6 |>
broom::glance() |>
tidyr::pivot_longer(dplyr::everything()) |>
md_named_tibble()maper_mpepr_gam_6 model.
| Value | |
|---|---|
| df | 12.0000000000 |
| logLik | 121681.2905335242 |
| AIC | -243336.5810670483 |
| BIC | -243218.9687010893 |
| deviance | 64886.5484799459 |
| df.residual | 62750.0000000000 |
| nobs | 62762.0000000000 |
| adj.r.squared | -0.0005918146 |
| npar | 12.0000000000 |
Source: Created by the authors.
Code
maper_mpepr_gam_6 |>
summarise_coefs() |>
md_named_tibble()maper_mpepr_gam_6 model.
| Value | |
|---|---|
| [Mean] | -0.1790218116 |
| (Intercept) | -2.9436585686 |
| year2009 | 0.0793258356 |
| year2010 | 0.1204258006 |
| year2011 | 0.0436141695 |
| year2012 | 0.0352971701 |
| year2013 | 0.0593406827 |
| year2014 | 0.0529859157 |
| year2015 | 0.0721808446 |
| year2016 | 0.1418366420 |
| year2017 | 0.1952237764 |
| year2018 | 0.0134687055 |
| year2019 | -0.0183027132 |
Source: Created by the authors.
Code
maper_mpepr_gam_6 |> mgcViz::getViz() |> mgcViz::check.gamViz()
#>
#> Method: REML Optimizer: outer newton
#> full convergence after 4 iterations.
#> Gradient range [0.132207848,0.132207848]
#> (score -121638.1214 & scale 1).
#> Hessian positive definite, eigenvalue range [26961.29141,26961.29141].
#> Model rank = 12 / 12
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.Code
dplyr::mutate(data, year = factor(year, ordered = FALSE)) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam(
model = maper_mpepr_gam_6,
type = 6,
x_label = "Years",
y_label = "Predicted probability of MAPER & MPEPR"
)maper_mpepr_gam_6 model. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
Model Results by MISFS-R Clusters
By s(spei_12m) + s(gdp_per_capita) + s(year, bs = "re") (Continuous year)
Code
mbepr_gam_1_by_misfs <-
dplyr::mutate(data, year = as.integer(as.character(year))) |>
gam_misfs(mbepr ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = 're'))dplyr::mutate(data, year = as.integer(as.character(year))) |>
summarise_gam_misfs(mbepr_gam_1_by_misfs)
#>
#> ── Model A ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(18.474)
#> Link function: logit
#>
#> Formula:
#> mbepr ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = "re")
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.77050143 0.02238914 -123.7431 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 3.585424039145 4.506802 50.28722 < 2.22e-16 ***
#> s(gdp_per_capita) 6.325078765838 7.463139 30.61648 0.00012567 ***
#> s(year) 0.000007142564 1.000000 0.00098 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = -0.000487 Deviance explained = 1.22%
#> -REML = -13357 Scale est. = 1 n = 7271
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.091050995e+1
#> 2 logLik 1.338233071e+4
#> 3 AIC -2.673672152e+4
#> 4 BIC -2.664044549e+4
#> 5 deviance 7.444556183e+3
#> 6 df.residual 7.260089490e+3
#> 7 nobs 7.271000000e+3
#> 8 adj.r.squared -4.873290164e-4
#> 9 npar 2 e+1
#>
#> ── Model B ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(16.824)
#> Link function: logit
#>
#> Formula:
#> mbepr ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = "re")
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.079223123 0.007943255 -387.6526 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 7.463785332006 8.434566 203.62496 < 2.22e-16 ***
#> s(gdp_per_capita) 8.388424661548 8.881697 262.46921 < 2.22e-16 ***
#> s(year) 0.000002408109 1.000000 0.00049 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = -0.000775 Deviance explained = 1.47%
#> -REML = -62596 Scale est. = 1 n = 29045
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.685221240e+1
#> 2 logLik 6.264328753e+4
#> 3 AIC -1.252479425e+5
#> 4 BIC -1.250880695e+5
#> 5 deviance 3.064180952e+4
#> 6 df.residual 2.902814779e+4
#> 7 nobs 2.9045000 e+4
#> 8 adj.r.squared -7.750953394e-4
#> 9 npar 2 e+1
#>
#> ── Model C ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(40.074)
#> Link function: logit
#>
#> Formula:
#> mbepr ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = "re")
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.61784753 0.01350421 -193.8542 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 8.185619968319 8.824611 83.42890 < 2.22e-16 ***
#> s(gdp_per_capita) 8.779018990738 8.984698 289.37065 < 2.22e-16 ***
#> s(year) 0.000008673734 1.000000 0.00014 0.000070913 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0408 Deviance explained = 3%
#> -REML = -35893 Scale est. = 1 n = 18633
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 4.079981636e-2 weak cohen1988
#> 2 SE 2.717354051e-3 <NA> <NA>
#> 3 Lower CI 3.547390028e-2 weak cohen1988
#> 4 Upper CI 4.612573243e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.796464763e+1
#> 2 logLik 3.594746970e+4
#> 3 AIC -7.185532075e+4
#> 4 BIC -7.170016045e+4
#> 5 deviance 1.813362262e+4
#> 6 df.residual 1.861503535e+4
#> 7 nobs 1.863300000e+4
#> 8 adj.r.squared 4.079981636e-2
#> 9 npar 2 e+1
#>
#> ── Model D ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(37.043)
#> Link function: logit
#>
#> Formula:
#> mbepr ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = "re")
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.28660135 0.02392335 -95.5803 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 3.869415025716 4.856561 13.08541 0.021844 *
#> s(gdp_per_capita) 7.508511900702 8.408435 207.78266 < 2e-16 ***
#> s(year) 0.000007236705 1.000000 0.00000 0.511048
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.086 Deviance explained = 9.78%
#> -REML = -4347.1 Scale est. = 1 n = 2538
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0.08597159417 weak cohen1988
#> 2 SE 0.01016400052 <NA> <NA>
#> 3 Lower CI 0.06605051921 weak cohen1988
#> 4 Upper CI 0.1058926691 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.237793416e+1
#> 2 logLik 4.377235198e+3
#> 3 AIC -8.723982867e+3
#> 4 BIC -8.634972518e+3
#> 5 deviance 2.454448364e+3
#> 6 df.residual 2.525622066e+3
#> 7 nobs 2.5380 e+3
#> 8 adj.r.squared 8.597159417e-2
#> 9 npar 2 e+1Code
mbepr_gam_1_by_misfs |>
summarise_coefs_misfs() |>
md_named_tibble()mbepr_gam_1_by_misfs model.
| A | B | C | D | |
|---|---|---|---|---|
| [Mean] | -0.1310537568 | -0.1577685877 | -0.3738963240 | -0.5898886872 |
| (Intercept) | -2.7705014320 | -3.0792231234 | -2.6178475305 | -2.2866013524 |
| mean(s(spei_12m)) | -0.0012567827 | 0.0142475960 | 0.0052501770 | 0.0062860207 |
| mean(s(gdp_per_capita)) | 0.0178596693 | -0.0227085623 | -0.5452589573 | -1.0630829510 |
| mean(s(year)) | 0.0000003165 | 0.0000000669 | 0.0000000742 | -0.0000000186 |
Source: Created by the authors.
Code
dplyr::mutate(data, year = as.integer(as.character(year))) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam_misfs(
gam_models = mbepr_gam_1_by_misfs,
type = 1,
x_label = "Standardised Precipitation Evapotranspiration Index (12 months)",
y_label = "Predicted probability of MBEPR"
)mbepr_gam_1_by_misfs model. All other variables are held constant at their mean values except SPEI. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
Code
beipr_gam_1_by_misfs <-
dplyr::mutate(data, year = as.integer(as.character(year))) |>
gam_misfs(beipr ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = 're'))dplyr::mutate(data, year = as.integer(as.character(year))) |>
summarise_gam_misfs(beipr_gam_1_by_misfs)
#>
#> ── Model A ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(25.478)
#> Link function: logit
#>
#> Formula:
#> beipr ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = "re")
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.65185711 0.02206313 -120.1941 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 6.693819283232 7.864433 88.80543 < 2.22e-16 ***
#> s(gdp_per_capita) 7.883052707882 8.661109 45.75864 < 2.22e-16 ***
#> s(year) 0.000009250345 1.000000 0.00205 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0106 Deviance explained = 1.8%
#> -REML = -13098 Scale est. = 1 n = 7271
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 1.059458631e-2 very weak (negligible) cohen1988
#> 2 SE 2.285067766e-3 <NA> <NA>
#> 3 Lower CI 6.115935782e-3 very weak (negligible) cohen1988
#> 4 Upper CI 1.507323683e-2 very weak (negligible) cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.557688124e+1
#> 2 logLik 1.313629340e+4
#> 3 AIC -2.623575478e+4
#> 4 BIC -2.610883805e+4
#> 5 deviance 7.376756920e+3
#> 6 df.residual 7.255423119e+3
#> 7 nobs 7.271000000e+3
#> 8 adj.r.squared 1.059458631e-2
#> 9 npar 2 e+1
#>
#> ── Model B ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(23.911)
#> Link function: logit
#>
#> Formula:
#> beipr ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = "re")
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.854708408 0.007573918 -376.913 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 7.77860683719 8.626997 180.04109 < 2.22e-16 ***
#> s(gdp_per_capita) 8.54053036718 8.931484 253.93093 < 2.22e-16 ***
#> s(year) 0.00000328935 1.000000 0.00125 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = -0.00596 Deviance explained = 1.37%
#> -REML = -56307 Scale est. = 1 n = 29045
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.731914049e+1
#> 2 logLik 5.635651747e+4
#> 3 AIC -1.126739180e+5
#> 4 BIC -1.125120401e+5
#> 5 deviance 3.031151833e+4
#> 6 df.residual 2.902768086e+4
#> 7 nobs 2.9045000 e+4
#> 8 adj.r.squared -5.956767481e-3
#> 9 npar 2 e+1
#>
#> ── Model C ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(75.056)
#> Link function: logit
#>
#> Formula:
#> beipr ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = "re")
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.511152305 0.008421084 -298.1982 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 8.428944876816 8.910947 55.18369 < 2.22e-16 ***
#> s(gdp_per_capita) 8.882571386492 8.995635 698.45008 < 2.22e-16 ***
#> s(year) 0.000006025711 1.000000 0.00069 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0716 Deviance explained = 4.86%
#> -REML = -39633 Scale est. = 1 n = 18633
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 7.160714322e-2 weak cohen1988
#> 2 SE 3.484318398e-3 <NA> <NA>
#> 3 Lower CI 6.477800465e-2 weak cohen1988
#> 4 Upper CI 7.843628180e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.831152229e+1
#> 2 logLik 3.969298039e+4
#> 3 AIC -7.934615251e+4
#> 4 BIC -7.919024958e+4
#> 5 deviance 1.837032349e+4
#> 6 df.residual 1.861468848e+4
#> 7 nobs 1.863300000e+4
#> 8 adj.r.squared 7.160714322e-2
#> 9 npar 2 e+1
#>
#> ── Model D ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(57.251)
#> Link function: logit
#>
#> Formula:
#> beipr ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = "re")
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -1.9420231 0.0371683 -52.24944 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 2.11088702959 2.689219 6.66103 0.061442 .
#> s(gdp_per_capita) 7.68632005188 8.528509 246.95261 < 2.22e-16 ***
#> s(year) 0.00003913388 1.000000 0.00059 0.000081652 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.121 Deviance explained = 11.1%
#> -REML = -4420.4 Scale est. = 1 n = 2538
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0.1206707823 weak cohen1988
#> 2 SE 0.01158457389 <NA> <NA>
#> 3 Lower CI 0.09796543472 weak cohen1988
#> 4 Upper CI 0.1433761299 moderate cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.079724622e+1
#> 2 logLik 4.449238644e+3
#> 3 AIC -8.872041678e+3
#> 4 BIC -8.794861175e+3
#> 5 deviance 2.490273656e+3
#> 6 df.residual 2.527202754e+3
#> 7 nobs 2.5380 e+3
#> 8 adj.r.squared 1.206707823e-1
#> 9 npar 2 e+1Code
beipr_gam_1_by_misfs |>
summarise_coefs_misfs() |>
md_named_tibble()beipr_gam_1_by_misfs model.
| A | B | C | D | |
|---|---|---|---|---|
| [Mean] | -0.1409376509 | -0.1546389653 | -0.3440311558 | -0.2527573118 |
| (Intercept) | -2.6518571118 | -2.8547084085 | -2.5111523048 | -1.9420231027 |
| mean(s(spei_12m)) | -0.0182165492 | -0.0144422976 | -0.0118655437 | -0.0064051561 |
| mean(s(gdp_per_capita)) | -0.0003274917 | -0.0120100365 | -0.4736312245 | -0.3394974630 |
| mean(s(year)) | 0.0000004614 | 0.0000001085 | 0.0000001021 | 0.0000004395 |
Source: Created by the authors.
Code
dplyr::mutate(data, year = as.integer(as.character(year))) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam_misfs(
gam_models = beipr_gam_1_by_misfs,
type = 1,
x_label = "Standardised Precipitation Evapotranspiration Index (12 months)",
y_label = "Predicted probability of BEIPR"
)beipr_gam_1_by_misfs model. All other variables are held constant at their mean values except SPEI. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
Code
mbepr_beipr_gam_1_by_misfs <-
dplyr::mutate(data, year = as.integer(as.character(year))) |>
gam_misfs(mbepr_beipr ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = 're'))dplyr::mutate(data, year = as.integer(as.character(year))) |>
summarise_gam_misfs(mbepr_beipr_gam_1_by_misfs)
#>
#> ── Model A ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(17.655)
#> Link function: logit
#>
#> Formula:
#> mbepr_beipr ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = "re")
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -1.93257846 0.02271077 -85.09524 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 3.42848021188 4.316045 37.04845 0.00000045315 ***
#> s(gdp_per_capita) 8.14470663511 8.794077 127.90062 < 2.22e-16 ***
#> s(year) 0.00001166075 1.000000 0.00170 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0317 Deviance explained = 2.04%
#> -REML = -9131.6 Scale est. = 1 n = 7271
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 3.171548474e-2 weak cohen1988
#> 2 SE 3.869202535e-3 <NA> <NA>
#> 3 Lower CI 2.413198712e-2 weak cohen1988
#> 4 Upper CI 3.929898236e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.257319851e+1
#> 2 logLik 9.164375876e+3
#> 3 AIC -1.829853146e+4
#> 4 BIC -1.819439764e+4
#> 5 deviance 7.104669417e+3
#> 6 df.residual 7.258426801e+3
#> 7 nobs 7.271000000e+3
#> 8 adj.r.squared 3.171548474e-2
#> 9 npar 2 e+1
#>
#> ── Model B ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(16.785)
#> Link function: logit
#>
#> Formula:
#> mbepr_beipr ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = "re")
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.211168972 0.007619051 -290.2158 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 5.014045657309 6.164648 86.90427 < 2.22e-16 ***
#> s(gdp_per_capita) 8.584881359620 8.943785 364.57630 < 2.22e-16 ***
#> s(year) 0.000003923522 1.000000 0.00067 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.00542 Deviance explained = 1.5%
#> -REML = -40828 Scale est. = 1 n = 29045
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 5.420143243e-3 very weak (negligible) cohen1988
#> 2 SE 8.219347763e-4 <NA> <NA>
#> 3 Lower CI 3.809180684e-3 very weak (negligible) cohen1988
#> 4 Upper CI 7.031105802e-3 very weak (negligible) cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.459893094e+1
#> 2 logLik 4.087086004e+4
#> 3 AIC -8.170818123e+4
#> 4 BIC -8.156938733e+4
#> 5 deviance 2.914897765e+4
#> 6 df.residual 2.903040107e+4
#> 7 nobs 2.9045000 e+4
#> 8 adj.r.squared 5.420143243e-3
#> 9 npar 2 e+1
#>
#> ── Model C ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(33.992)
#> Link function: logit
#>
#> Formula:
#> mbepr_beipr ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = "re")
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -1.78883251 0.01398642 -127.8979 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 8.56916723716 8.948355 110.67072 < 2.22e-16 ***
#> s(gdp_per_capita) 8.87477219826 8.995034 668.39868 < 2.22e-16 ***
#> s(year) 0.00001452181 1.000000 0.00031 0.0000042037 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0706 Deviance explained = 5.89%
#> -REML = -27025 Scale est. = 1 n = 18633
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 7.056625750e-2 weak cohen1988
#> 2 SE 3.462779580e-3 <NA> <NA>
#> 3 Lower CI 6.377933424e-2 weak cohen1988
#> 4 Upper CI 7.735318077e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.844395396e+1
#> 2 logLik 2.708600770e+4
#> 3 AIC -5.413215531e+4
#> 4 BIC -5.397604944e+4
#> 5 deviance 1.818590945e+4
#> 6 df.residual 1.861455605e+4
#> 7 nobs 1.863300000e+4
#> 8 adj.r.squared 7.056625750e-2
#> 9 npar 2 e+1
#>
#> ── Model D ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(26.729)
#> Link function: logit
#>
#> Formula:
#> mbepr_beipr ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = "re")
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -1.27696464 0.01671877 -76.37913 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 1.003995035362 1.007977 7.70323 0.0056066 **
#> s(gdp_per_capita) 8.035081674469 8.732283 312.47450 < 2.22e-16 ***
#> s(year) 0.000004297156 1.000000 0.00000 0.5280488
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.138 Deviance explained = 13.6%
#> -REML = -2910.4 Scale est. = 1 n = 2538
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0.1376428267 moderate cohen1988
#> 2 SE 0.01213365012 <NA> <NA>
#> 3 Lower CI 0.1138613094 weak cohen1988
#> 4 Upper CI 0.1614243439 moderate cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.003908101e+1
#> 2 logLik 2.939160515e+3
#> 3 AIC -5.855273924e+3
#> 4 BIC -5.787986380e+3
#> 5 deviance 2.466337895e+3
#> 6 df.residual 2.527960919e+3
#> 7 nobs 2.5380 e+3
#> 8 adj.r.squared 1.376428267e-1
#> 9 npar 2 e+1Code
mbepr_beipr_gam_1_by_misfs |>
summarise_coefs_misfs() |>
md_named_tibble()mbepr_beipr_gam_1_by_misfs model.
| A | B | C | D | |
|---|---|---|---|---|
| [Mean] | -0.0880911859 | -0.1136614951 | -0.3539310117 | -0.4014485517 |
| (Intercept) | -1.9325784643 | -2.2111689717 | -1.7888325091 | -1.2769646427 |
| mean(s(spei_12m)) | 0.0057724696 | 0.0172598259 | -0.0186608780 | 0.0029059069 |
| mean(s(gdp_per_capita)) | 0.0132002314 | -0.0241554939 | -0.5690933268 | -0.7531288403 |
| mean(s(year)) | 0.0000004385 | 0.0000000817 | 0.0000001189 | 0.0000000091 |
Source: Created by the authors.
Code
dplyr::mutate(data, year = as.integer(as.character(year))) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam_misfs(
gam_models = mbepr_beipr_gam_1_by_misfs,
type = 1,
x_label = "Standardised Precipitation Evapotranspiration Index (12 months)",
y_label = "Predicted probability of MBEPR & BEIPR"
)
#> Warning: Removed 500 rows containing missing values or values outside the scale range
#> (`geom_line()`).
#> Warning in max(ids, na.rm = TRUE): no non-missing arguments to max;
#> returning -Infmbepr_beipr_gam_1_by_misfs model. All other variables are held constant at their mean values except SPEI. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
Code
maper_gam_1_by_misfs <-
dplyr::mutate(data, year = as.integer(as.character(year))) |>
gam_misfs(maper ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = 're'))dplyr::mutate(data, year = as.integer(as.character(year))) |>
summarise_gam_misfs(maper_gam_1_by_misfs)
#>
#> ── Model A ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(23.788)
#> Link function: logit
#>
#> Formula:
#> maper ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = "re")
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.5356317 0.0158056 -223.6948 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 4.5893046096 5.706236 38.24618 0.0000033879 ***
#> s(gdp_per_capita) 1.0317601522 1.062841 23.44288 0.0000024605 ***
#> s(year) 0.0000023952 1.000000 0.00002 0.0079066 **
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.00251 Deviance explained = 0.855%
#> -REML = -19053 Scale est. = 1 n = 7271
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 2.510767999e-3 very weak (negligible) cohen1988
#> 2 SE 1.121487168e-3 <NA> <NA>
#> 3 Lower CI 3.126935414e-4 very weak (negligible) cohen1988
#> 4 Upper CI 4.708842457e-3 very weak (negligible) cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 6.621067157e+0
#> 2 logLik 1.906999933e+4
#> 3 AIC -3.812246049e+4
#> 4 BIC -3.806202705e+4
#> 5 deviance 7.720296853e+3
#> 6 df.residual 7.264378933e+3
#> 7 nobs 7.271000000e+3
#> 8 adj.r.squared 2.510767999e-3
#> 9 npar 2 e+1
#>
#> ── Model B ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(24.131)
#> Link function: logit
#>
#> Formula:
#> maper ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = "re")
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.972477788 0.008077985 -491.7659 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 8.268887699852 8.857245 387.99400 < 2.22e-16 ***
#> s(gdp_per_capita) 8.757532927345 8.980289 625.05095 < 2.22e-16 ***
#> s(year) 0.000002009526 1.000000 0.00032 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0176 Deviance explained = 2.89%
#> -REML = -96217 Scale est. = 1 n = 29045
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 1.757998579e-2 very weak (negligible) cohen1988
#> 2 SE 1.462173054e-3 <NA> <NA>
#> 3 Lower CI 1.471417927e-2 very weak (negligible) cohen1988
#> 4 Upper CI 2.044579232e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.802642264e+1
#> 2 logLik 9.627230596e+4
#> 3 AIC -1.925049368e+5
#> 4 BIC -1.923407494e+5
#> 5 deviance 3.130296675e+4
#> 6 df.residual 2.902697358e+4
#> 7 nobs 2.9045000 e+4
#> 8 adj.r.squared 1.757998579e-2
#> 9 npar 2 e+1
#>
#> ── Model C ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(53.326)
#> Link function: logit
#>
#> Formula:
#> maper ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = "re")
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.416535448 0.006704826 -509.5636 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 7.4054453196514 8.391900 117.80611 < 2e-16 ***
#> s(gdp_per_capita) 7.5742349443957 8.479155 95.62161 < 2e-16 ***
#> s(year) 0.0000008288421 1.000000 0.00000 0.46555
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.012 Deviance explained = 1.41%
#> -REML = -47083 Scale est. = 1 n = 18633
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 1.203325991e-2 very weak (negligible) cohen1988
#> 2 SE 1.519993892e-3 <NA> <NA>
#> 3 Lower CI 9.054126623e-3 very weak (negligible) cohen1988
#> 4 Upper CI 1.501239320e-2 very weak (negligible) cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.597968109e+1
#> 2 logLik 4.712419551e+4
#> 3 AIC -9.421227623e+4
#> 4 BIC -9.407083823e+4
#> 5 deviance 1.837882892e+4
#> 6 df.residual 1.861702032e+4
#> 7 nobs 1.863300000e+4
#> 8 adj.r.squared 1.203325991e-2
#> 9 npar 2 e+1
#>
#> ── Model D ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(88.727)
#> Link function: logit
#>
#> Formula:
#> maper ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = "re")
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.52935083 0.03553781 -99.31256 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 1.00564979661 1.011276 0.19445 0.66188
#> s(gdp_per_capita) 2.51292258833 3.079325 30.39445 0.0000017258 ***
#> s(year) 0.00001868132 1.000000 0.00034 0.0000140167 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0114 Deviance explained = 1.52%
#> -REML = -6989.5 Scale est. = 1 n = 2538
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 1.136599182e-2 very weak (negligible) cohen1988
#> 2 SE 3.997299703e-3 <NA> <NA>
#> 3 Lower CI 3.531428370e-3 very weak (negligible) cohen1988
#> 4 Upper CI 1.920055527e-2 very weak (negligible) cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 4.518591066e+0
#> 2 logLik 7.002134517e+3
#> 3 AIC -1.399208776e+4
#> 4 BIC -1.395652373e+4
#> 5 deviance 2.482532032e+3
#> 6 df.residual 2.533481409e+3
#> 7 nobs 2.5380 e+3
#> 8 adj.r.squared 1.136599182e-2
#> 9 npar 2 e+1Code
maper_gam_1_by_misfs |>
summarise_coefs_misfs() |>
md_named_tibble()maper_gam_1_by_misfs model.
| A | B | C | D | |
|---|---|---|---|---|
| [Mean] | -0.1685132319 | -0.2808048715 | -0.2458539480 | -0.1990209933 |
| (Intercept) | -3.5356316830 | -3.9724777883 | -3.4165354476 | -3.5293508271 |
| mean(s(spei_12m)) | 0.0241968394 | -0.0603534674 | -0.0383885557 | 0.0005774613 |
| mean(s(gdp_per_capita)) | -0.0058227261 | -0.1222709431 | -0.1283385011 | -0.0506962091 |
| mean(s(year)) | 0.0000000245 | 0.0000000534 | -0.0000000015 | -0.0000003081 |
Source: Created by the authors.
Code
dplyr::mutate(data, year = as.integer(as.character(year))) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam_misfs(
gam_models = maper_gam_1_by_misfs,
type = 1,
x_label = "Standardised Precipitation Evapotranspiration Index (12 months)",
y_label = "Predicted probability of MAPER"
)maper_gam_1_by_misfs model. All other variables are held constant at their mean values except SPEI. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
Code
mpepr_gam_1_by_misfs <-
dplyr::mutate(data, year = as.integer(as.character(year))) |>
gam_misfs(mpepr ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = 're'))dplyr::mutate(data, year = as.integer(as.character(year))) |>
summarise_gam_misfs(mpepr_gam_1_by_misfs)
#>
#> ── Model A ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(31.492)
#> Link function: logit
#>
#> Formula:
#> mpepr ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = "re")
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.42171787 0.02200123 -155.524 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 4.901310949050 6.062783 97.02856 < 2.22e-16 ***
#> s(gdp_per_capita) 1.006806659711 1.013579 18.57059 0.000017802 ***
#> s(year) 0.000007798031 1.000000 0.00044 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = -0.00426 Deviance explained = 1.5%
#> -REML = -17852 Scale est. = 1 n = 7271
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 6.908125407e+0
#> 2 logLik 1.786925380e+4
#> 3 AIC -3.572035485e+4
#> 4 BIC -3.565780364e+4
#> 5 deviance 7.697729939e+3
#> 6 df.residual 7.264091875e+3
#> 7 nobs 7.271000000e+3
#> 8 adj.r.squared -4.262616913e-3
#> 9 npar 2 e+1
#>
#> ── Model B ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(27.018)
#> Link function: logit
#>
#> Formula:
#> mpepr ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = "re")
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.756149891 0.007929237 -473.7088 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 8.73936069544 8.980595 669.27120 < 2.22e-16 ***
#> s(gdp_per_capita) 8.81134347763 8.987925 620.74023 < 2.22e-16 ***
#> s(year) 0.00000223106 1.000000 0.00085 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0183 Deviance explained = 3.62%
#> -REML = -83726 Scale est. = 1 n = 29045
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 1.834240151e-2 very weak (negligible) cohen1988
#> 2 SE 1.492383522e-3 <NA> <NA>
#> 3 Lower CI 1.541738355e-2 very weak (negligible) cohen1988
#> 4 Upper CI 2.126741946e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.855070640e+1
#> 2 logLik 8.378651351e+4
#> 3 AIC -1.675330900e+5
#> 4 BIC -1.673678184e+5
#> 5 deviance 3.189575842e+4
#> 6 df.residual 2.902644929e+4
#> 7 nobs 2.9045000 e+4
#> 8 adj.r.squared 1.834240151e-2
#> 9 npar 2 e+1
#>
#> ── Model C ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(91.848)
#> Link function: logit
#>
#> Formula:
#> mpepr ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = "re")
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.339089402 0.008509168 -392.4108 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 6.891909534387 8.004560 280.0341 < 2e-16 ***
#> s(gdp_per_capita) 8.237933381112 8.833265 317.3883 < 2e-16 ***
#> s(year) 0.000003678689 1.000000 0.0000 0.70503
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0283 Deviance explained = 2.71%
#> -REML = -49444 Scale est. = 1 n = 18633
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 2.832588693e-2 weak cohen1988
#> 2 SE 2.293613632e-3 <NA> <NA>
#> 3 Lower CI 2.383048681e-2 weak cohen1988
#> 4 Upper CI 3.282128704e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.612984659e+1
#> 2 logLik 4.948834438e+4
#> 3 AIC -9.894100828e+4
#> 4 BIC -9.880127123e+4
#> 5 deviance 1.849755522e+4
#> 6 df.residual 1.861687015e+4
#> 7 nobs 1.863300000e+4
#> 8 adj.r.squared 2.832588693e-2
#> 9 npar 2 e+1
#>
#> ── Model D ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(117.87)
#> Link function: logit
#>
#> Formula:
#> mpepr ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = "re")
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.32148211 0.03506225 -94.73099 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 1.00549632000 1.010968 0.27960 0.60056231
#> s(gdp_per_capita) 3.13582851928 3.835153 19.32045 0.00079322 ***
#> s(year) 0.00002728347 1.000000 0.00005 0.17655944
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.00716 Deviance explained = 0.87%
#> -REML = -6953.1 Scale est. = 1 n = 2538
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 7.162192381e-3 very weak (negligible) cohen1988
#> 2 SE 3.186609114e-3 <NA> <NA>
#> 3 Lower CI 9.165532851e-4 very weak (negligible) cohen1988
#> 4 Upper CI 1.340783148e-2 very weak (negligible) cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 5.141352123e+0
#> 2 logLik 6.967705233e+3
#> 3 AIC -1.392171812e+4
#> 4 BIC -1.388174240e+4
#> 5 deviance 2.496202603e+3
#> 6 df.residual 2.532858648e+3
#> 7 nobs 2.5380 e+3
#> 8 adj.r.squared 7.162192381e-3
#> 9 npar 2 e+1Code
mpepr_gam_1_by_misfs |>
summarise_coefs_misfs() |>
md_named_tibble()mpepr_gam_1_by_misfs model.
| A | B | C | D | |
|---|---|---|---|---|
| [Mean] | -0.1682457248 | -0.2936806231 | -0.1928735196 | -0.1780537093 |
| (Intercept) | -3.4217178726 | -3.7561498915 | -3.3390894022 | -3.3214821061 |
| mean(s(spei_12m)) | 0.0110289389 | -0.0694069958 | 0.0372264957 | -0.0005493428 |
| mean(s(gdp_per_capita)) | -0.0047174756 | -0.1658666328 | -0.0948243838 | -0.0260719865 |
| mean(s(year)) | 0.0000002064 | 0.0000000870 | 0.0000000027 | -0.0000001162 |
Source: Created by the authors.
Code
dplyr::mutate(data, year = as.integer(as.character(year))) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam_misfs(
gam_models = mpepr_gam_1_by_misfs,
type = 1,
x_label = "Standardised Precipitation Evapotranspiration Index (12 months)",
y_label = "Predicted probability of MPEPR"
)mpepr_gam_1_by_misfs model. All other variables are held constant at their mean values except SPEI. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
Code
maper_mpepr_gam_1_by_misfs <-
dplyr::mutate(data, year = as.integer(as.character(year))) |>
gam_misfs(maper_mpepr ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = 're'))dplyr::mutate(data, year = as.integer(as.character(year))) |>
summarise_gam_misfs(maper_mpepr_gam_1_by_misfs)
#>
#> ── Model A ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(24.016)
#> Link function: logit
#>
#> Formula:
#> maper_mpepr ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = "re")
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.74708724 0.02208828 -124.3685 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 4.356448950241 5.432914 81.01741 < 2.22e-16 ***
#> s(gdp_per_capita) 6.686677834810 7.786549 85.81369 < 2.22e-16 ***
#> s(year) 0.000008411868 1.000000 0.00008 0.0018389 **
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0107 Deviance explained = 2.14%
#> -REML = -13503 Scale est. = 1 n = 7271
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 1.068843752e-2 very weak (negligible) cohen1988
#> 2 SE 2.294948777e-3 <NA> <NA>
#> 3 Lower CI 6.190420575e-3 very weak (negligible) cohen1988
#> 4 Upper CI 1.518645447e-2 very weak (negligible) cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.204313520e+1
#> 2 logLik 1.353128848e+4
#> 3 AIC -2.703213800e+4
#> 4 BIC -2.692725068e+4
#> 5 deviance 7.330433443e+3
#> 6 df.residual 7.258956865e+3
#> 7 nobs 7.271000000e+3
#> 8 adj.r.squared 1.068843752e-2
#> 9 npar 2 e+1
#>
#> ── Model B ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(19.319)
#> Link function: logit
#>
#> Formula:
#> maper_mpepr ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = "re")
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.147149555 0.007875411 -399.6172 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 8.715106867971 8.976908 538.95271 < 2.22e-16 ***
#> s(gdp_per_capita) 8.839999026864 8.991296 946.61224 < 2.22e-16 ***
#> s(year) 0.000002489889 1.000000 0.00071 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0306 Deviance explained = 4.29%
#> -REML = -64333 Scale est. = 1 n = 29045
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 3.059080760e-2 weak cohen1988
#> 2 SE 1.903245973e-3 <NA> <NA>
#> 3 Lower CI 2.686051404e-2 weak cohen1988
#> 4 Upper CI 3.432110116e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.855510838e+1
#> 2 logLik 6.439471404e+4
#> 3 AIC -1.287494917e+5
#> 4 BIC -1.285842227e+5
#> 5 deviance 3.096481031e+4
#> 6 df.residual 2.902644489e+4
#> 7 nobs 2.9045000 e+4
#> 8 adj.r.squared 3.059080760e-2
#> 9 npar 2 e+1
#>
#> ── Model C ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(49.428)
#> Link function: logit
#>
#> Formula:
#> maper_mpepr ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = "re")
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.64745440 0.01338266 -197.8273 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 7.09881348326 8.169223 150.60108 < 2.22e-16 ***
#> s(gdp_per_capita) 8.23818405264 8.834190 330.69599 < 2.22e-16 ***
#> s(year) 0.00001039964 1.000000 0.00019 0.00001504 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0266 Deviance explained = 2.79%
#> -REML = -37690 Scale est. = 1 n = 18633
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 2.659238110e-2 weak cohen1988
#> 2 SE 2.226287378e-3 <NA> <NA>
#> 3 Lower CI 2.222893802e-2 weak cohen1988
#> 4 Upper CI 3.095582418e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.633700794e+1
#> 2 logLik 3.773401075e+4
#> 3 AIC -7.543194088e+4
#> 4 BIC -7.529063673e+4
#> 5 deviance 1.823814964e+4
#> 6 df.residual 1.861666299e+4
#> 7 nobs 1.863300000e+4
#> 8 adj.r.squared 2.659238110e-2
#> 9 npar 2 e+1
#>
#> ── Model D ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(62.45)
#> Link function: logit
#>
#> Formula:
#> maper_mpepr ~ s(spei_12m) + s(gdp_per_capita) + s(year, bs = "re")
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.69322922 0.03597916 -74.85526 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 1.00292377092 1.005840 0.01478 0.91504
#> s(gdp_per_capita) 3.03758135292 3.716898 31.89257 0.000001759 ***
#> s(year) 0.00002696957 1.000000 0.00049 0.000012732 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0128 Deviance explained = 1.51%
#> -REML = -5427.1 Scale est. = 1 n = 2538
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 1.278503174e-2 very weak (negligible) cohen1988
#> 2 SE 4.233408063e-3 <NA> <NA>
#> 3 Lower CI 4.487704400e-3 very weak (negligible) cohen1988
#> 4 Upper CI 2.108235907e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 5.040532093e+0
#> 2 logLik 5.441295424e+3
#> 3 AIC -1.086914527e+4
#> 4 BIC -1.082989001e+4
#> 5 deviance 2.486096642e+3
#> 6 df.residual 2.532959468e+3
#> 7 nobs 2.5380 e+3
#> 8 adj.r.squared 1.278503174e-2
#> 9 npar 2 e+1Code
maper_mpepr_gam_1_by_misfs |>
summarise_coefs_misfs() |>
md_named_tibble()maper_mpepr_gam_1_by_misfs model.
| A | B | C | D | |
|---|---|---|---|---|
| [Mean] | -0.1678638760 | -0.2623331824 | -0.1531003304 | -0.1482940759 |
| (Intercept) | -2.7470872445 | -3.1471495549 | -2.6474544033 | -2.6932292198 |
| mean(s(spei_12m)) | 0.0212007584 | -0.0492554517 | 0.0793634771 | 0.0001434907 |
| mean(s(gdp_per_capita)) | -0.0889996881 | -0.1840239011 | -0.1254248235 | -0.0304381481 |
| mean(s(year)) | 0.0000000907 | 0.0000000809 | -0.0000000874 | -0.0000003822 |
Source: Created by the authors.
Code
dplyr::mutate(data, year = as.integer(as.character(year))) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam_misfs(
gam_models = maper_mpepr_gam_1_by_misfs,
type = 1,
x_label = "Standardised Precipitation Evapotranspiration Index (12 months)",
y_label = "Predicted probability of MAPER & MPEPR"
)maper_mpepr_gam_1_by_misfs model. All other variables are held constant at their mean values except SPEI. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
By s(spei_12m) + s(gdp_per_capita) + year (Ordered year)
In this model, the year variable is treated as a ordered categorical variable.
.L, .Q, and .C are, respectively, the coefficients for the ordered factor coded with linear, quadratic, and cubic contrasts.
data |>
summarise_gam_misfs(mbepr_gam_2_by_misfs)
#>
#> ── Model A ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(19.243)
#> Link function: logit
#>
#> Formula:
#> mbepr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.783316502 0.009229724 -301.56010 < 2.22e-16 ***
#> year.L 0.585106184 0.046026702 12.71232 < 2.22e-16 ***
#> year.Q -0.270247643 0.033412257 -8.08828 6.0514e-16 ***
#> year.C 0.064478614 0.031774257 2.02927 0.04243058 *
#> year^4 -0.018437103 0.033037270 -0.55807 0.57679672
#> year^5 0.154502582 0.038834044 3.97853 6.9341e-05 ***
#> year^6 -0.129285332 0.035011959 -3.69260 0.00022197 ***
#> year^7 0.030317969 0.031538419 0.96130 0.33639998
#> year^8 0.011989720 0.031318674 0.38283 0.70184601
#> year^9 -0.070206738 0.032468993 -2.16227 0.03059735 *
#> year^10 -0.094562752 0.030479180 -3.10254 0.00191870 **
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 4.213269 5.321403 19.62633 0.002229 **
#> s(gdp_per_capita) 7.983053 8.718735 136.86642 < 2e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = -0.0043 Deviance explained = 4.84%
#> -REML = -13461 Scale est. = 1 n = 7271
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.319632186e+1
#> 2 logLik 1.351835954e+4
#> 3 AIC -2.698515574e+4
#> 4 BIC -2.680747751e+4
#> 5 deviance 7.443829780e+3
#> 6 df.residual 7.247803678e+3
#> 7 nobs 7.271000000e+3
#> 8 adj.r.squared -4.304359701e-3
#> 9 npar 2.9 e+1
#>
#> ── Model B ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(17.174)
#> Link function: logit
#>
#> Formula:
#> mbepr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.085701791 0.005066000 -609.10018 < 2.22e-16 ***
#> year.L 0.256712505 0.023235181 11.04844 < 2.22e-16 ***
#> year.Q -0.295700427 0.017609063 -16.79251 < 2.22e-16 ***
#> year.C 0.001991815 0.017091874 0.11654 0.9072279
#> year^4 -0.052348046 0.017679257 -2.96099 0.0030666 **
#> year^5 0.072388339 0.018025970 4.01578 0.000059249400 ***
#> year^6 -0.058549096 0.019158522 -3.05603 0.0022429 **
#> year^7 0.056179019 0.017951308 3.12952 0.0017509 **
#> year^8 0.035104454 0.017349330 2.02339 0.0430330 *
#> year^9 -0.102398129 0.018149167 -5.64203 0.000000016806 ***
#> year^10 0.055423082 0.018618120 2.97684 0.0029124 **
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 8.332668 8.882537 131.9754 < 2.22e-16 ***
#> s(gdp_per_capita) 8.666506 8.963381 511.9798 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = -0.00906 Deviance explained = 3.19%
#> -REML = -62820 Scale est. = 1 n = 29045
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.799917357e+1
#> 2 logLik 6.290498951e+4
#> 3 AIC -1.257502872e+5
#> 4 BIC -1.255032644e+5
#> 5 deviance 3.063357529e+4
#> 6 df.residual 2.901700083e+4
#> 7 nobs 2.9045000 e+4
#> 8 adj.r.squared -9.063547776e-3
#> 9 npar 2.9 e+1
#>
#> ── Model C ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(40.229)
#> Link function: logit
#>
#> Formula:
#> mbepr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.618157766 0.004209328 -621.98944 < 2.22e-16 ***
#> year.L -0.006891703 0.031324953 -0.22001 0.82586585
#> year.Q 0.033355002 0.017496064 1.90643 0.05659458 .
#> year.C 0.022489152 0.015636385 1.43826 0.15036093
#> year^4 -0.042700954 0.015633174 -2.73143 0.00630597 **
#> year^5 0.056556444 0.015920777 3.55237 0.00038178 ***
#> year^6 -0.043163882 0.017829168 -2.42097 0.01547915 *
#> year^7 0.030243496 0.015136412 1.99806 0.04570989 *
#> year^8 0.090965618 0.022111232 4.11400 0.0000388861 ***
#> year^9 -0.089787710 0.017633080 -5.09200 0.0000003543 ***
#> year^10 -0.022125926 0.014467788 -1.52932 0.12618431
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 8.162494 8.819018 60.96357 < 2.22e-16 ***
#> s(gdp_per_capita) 8.797123 8.987155 235.09336 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.042 Deviance explained = 3.41%
#> -REML = -35898 Scale est. = 1 n = 18633
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 4.201543224e-2 weak cohen1988
#> 2 SE 2.754043533e-3 <NA> <NA>
#> 3 Lower CI 3.661760610e-2 weak cohen1988
#> 4 Upper CI 4.741325838e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.795961713e+1
#> 2 logLik 3.598537166e+4
#> 3 AIC -7.191113097e+4
#> 4 BIC -7.167766848e+4
#> 5 deviance 1.812816377e+4
#> 6 df.residual 1.860504038e+4
#> 7 nobs 1.863300000e+4
#> 8 adj.r.squared 4.201543224e-2
#> 9 npar 2.9 e+1
#>
#> ── Model D ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(37.383)
#> Link function: logit
#>
#> Formula:
#> mbepr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.28719843 0.01052534 -217.30391 < 2.22e-16 ***
#> year.L -0.05181967 0.04584864 -1.13023 0.2583778
#> year.Q 0.04350822 0.03891154 1.11813 0.2635109
#> year.C -0.02620339 0.03905398 -0.67095 0.5022503
#> year^4 0.02524931 0.03527213 0.71584 0.4740883
#> year^5 0.05682770 0.03899065 1.45747 0.1449867
#> year^6 -0.10874928 0.03558879 -3.05572 0.0022452 **
#> year^7 0.06490335 0.03592519 1.80663 0.0708207 .
#> year^8 0.10880219 0.03586327 3.03381 0.0024149 **
#> year^9 -0.11798075 0.03987974 -2.95841 0.0030923 **
#> year^10 -0.01933468 0.03759919 -0.51423 0.6070904
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 2.513916 3.221126 2.40512 0.45777
#> s(gdp_per_capita) 7.252433 8.226255 137.33956 < 2e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0877 Deviance explained = 10.8%
#> -REML = -4341 Scale est. = 1 n = 2538
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0.08772279128 weak cohen1988
#> 2 SE 0.01024732575 <NA> <NA>
#> 3 Lower CI 0.06763840187 weak cohen1988
#> 4 Upper CI 0.1078071807 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.076634920e+1
#> 2 logLik 4.391636743e+3
#> 3 AIC -8.736378724e+3
#> 4 BIC -8.599466376e+3
#> 5 deviance 2.448497468e+3
#> 6 df.residual 2.517233651e+3
#> 7 nobs 2.5380 e+3
#> 8 adj.r.squared 8.772279128e-2
#> 9 npar 2.9 e+1Code
mbepr_gam_2_by_misfs |>
summarise_coefs_misfs() |>
md_named_tibble()mbepr_gam_2_by_misfs model.
| A | B | C | D | |
|---|---|---|---|---|
| [Mean] | -0.0762934319 | -0.1210631041 | -0.2680437423 | -0.3958672150 |
| (Intercept) | -2.7833165024 | -3.0857017913 | -2.6181577659 | -2.2871984262 |
| year.L | 0.5851061842 | 0.2567125050 | -0.0068917029 | -0.0518196743 |
| year.Q | -0.2702476434 | -0.2957004271 | 0.0333550018 | 0.0435082161 |
| year.C | 0.0644786140 | 0.0019918154 | 0.0224891521 | -0.0262033933 |
| year^4 | -0.0184371026 | -0.0523480462 | -0.0427009535 | 0.0252493068 |
| year^5 | 0.1545025819 | 0.0723883394 | 0.0565564438 | 0.0568277022 |
| year^6 | -0.1292853321 | -0.0585490961 | -0.0431638824 | -0.1087492821 |
| year^7 | 0.0303179685 | 0.0561790187 | 0.0302434962 | 0.0649033490 |
| year^8 | 0.0119897197 | 0.0351044545 | 0.0909656185 | 0.1088021901 |
| year^9 | -0.0702067375 | -0.1023981295 | -0.0897877095 | -0.1179807511 |
| year^10 | -0.0945627517 | 0.0554230824 | -0.0221259262 | -0.0193346752 |
| mean(s(spei_12m)) | -0.0171356472 | 0.0117758792 | -0.0076226432 | 0.0017440117 |
| mean(s(gdp_per_capita)) | 0.0512635891 | -0.0555460728 | -0.5683829455 | -1.0204277669 |
Source: Created by the authors.
Code
data |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam_misfs(
gam_models = mbepr_gam_2_by_misfs,
type = 2,
x_label = "Standardised Precipitation Evapotranspiration Index (12 months)",
y_label = "Predicted probability of MBEPR"
)mbepr_gam_2_by_misfs model. All other variables are held constant at their mean values except SPEI. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
data |>
summarise_gam_misfs(beipr_gam_2_by_misfs)
#>
#> ── Model A ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(26.645)
#> Link function: logit
#>
#> Formula:
#> beipr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.662751589 0.008033784 -331.44425 < 2.22e-16 ***
#> year.L 0.658078337 0.040334652 16.31546 < 2.22e-16 ***
#> year.Q -0.153590318 0.029085699 -5.28061 0.00000012875 ***
#> year.C -0.031960277 0.027562628 -1.15955 0.2462316
#> year^4 0.042970181 0.028752331 1.49449 0.1350466
#> year^5 0.051616176 0.034503033 1.49599 0.1346564
#> year^6 -0.098671768 0.030880144 -3.19531 0.0013968 **
#> year^7 -0.031043600 0.027523614 -1.12789 0.2593665
#> year^8 0.049196052 0.027718704 1.77483 0.0759256 .
#> year^9 0.013720073 0.028706116 0.47795 0.6326862
#> year^10 0.024197231 0.026936913 0.89829 0.3690295
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 5.66093 6.914622 27.08158 0.00027339 ***
#> s(gdp_per_capita) 8.53392 8.934795 204.07291 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0241 Deviance explained = 5.81%
#> -REML = -13221 Scale est. = 1 n = 7271
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 2.413974465e-2 weak cohen1988
#> 2 SE 3.402019249e-3 <NA> <NA>
#> 3 Lower CI 1.747190945e-2 very weak (negligible) cohen1988
#> 4 Upper CI 3.080757986e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.519484923e+1
#> 2 logLik 1.328709678e+4
#> 3 AIC -2.651901920e+4
#> 4 BIC -2.632889805e+4
#> 5 deviance 7.384862076e+3
#> 6 df.residual 7.245805151e+3
#> 7 nobs 7.271000000e+3
#> 8 adj.r.squared 2.413974465e-2
#> 9 npar 2.9 e+1
#>
#> ── Model B ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(24.383)
#> Link function: logit
#>
#> Formula:
#> beipr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.859734521 0.004376121 -653.48617 < 2.22e-16 ***
#> year.L 0.319243545 0.020020539 15.94580 < 2.22e-16 ***
#> year.Q -0.134887648 0.015173725 -8.88955 < 2.22e-16 ***
#> year.C -0.041754244 0.014745325 -2.83169 0.00463022 **
#> year^4 -0.034909283 0.015207197 -2.29558 0.02170011 *
#> year^5 0.064729296 0.015535464 4.16655 0.0000309243264 ***
#> year^6 -0.061155288 0.016530673 -3.69950 0.00021602 ***
#> year^7 0.021920059 0.015419262 1.42160 0.15514172
#> year^8 0.040630638 0.015044203 2.70075 0.00691833 **
#> year^9 -0.052646878 0.015724256 -3.34813 0.00081358 ***
#> year^10 0.094261300 0.016126004 5.84530 0.0000000050566 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 8.010772 8.752246 66.94599 < 2.22e-16 ***
#> s(gdp_per_capita) 8.679349 8.966034 524.44912 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = -0.0314 Deviance explained = 3.1%
#> -REML = -56532 Scale est. = 1 n = 29045
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.769012098e+1
#> 2 logLik 5.661758801e+4
#> 3 AIC -1.131757395e+5
#> 4 BIC -1.129297731e+5
#> 5 deviance 3.031701357e+4
#> 6 df.residual 2.901730988e+4
#> 7 nobs 2.9045000 e+4
#> 8 adj.r.squared -3.144979397e-2
#> 9 npar 2.9 e+1
#>
#> ── Model C ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(75.981)
#> Link function: logit
#>
#> Formula:
#> beipr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.511663742 0.003066312 -819.11559 < 2.22e-16 ***
#> year.L 0.123671378 0.022958131 5.38682 0.0000000717141373 ***
#> year.Q 0.071346920 0.012745551 5.59779 0.0000000217101377 ***
#> year.C -0.005697127 0.011409574 -0.49933 0.617548
#> year^4 -0.023796490 0.011394602 -2.08840 0.036762 *
#> year^5 0.006420962 0.011575740 0.55469 0.579106
#> year^6 -0.091815115 0.012971250 -7.07836 0.0000000000014588 ***
#> year^7 0.012920365 0.010988564 1.17580 0.239674
#> year^8 0.068283787 0.016143760 4.22973 0.0000233969194195 ***
#> year^9 -0.018453499 0.012879825 -1.43274 0.151931
#> year^10 0.041276743 0.010589871 3.89776 0.0000970877865959 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 8.397573 8.903406 65.41918 < 2.22e-16 ***
#> s(gdp_per_capita) 8.899197 8.996804 637.63411 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0809 Deviance explained = 6.05%
#> -REML = -39713 Scale est. = 1 n = 18633
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 8.089570581e-2 weak cohen1988
#> 2 SE 3.666362476e-3 <NA> <NA>
#> 3 Lower CI 7.370976740e-2 weak cohen1988
#> 4 Upper CI 8.808164422e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.829676986e+1
#> 2 logLik 3.980828045e+4
#> 3 AIC -7.955676047e+4
#> 4 BIC -7.932256141e+4
#> 5 deviance 1.836583071e+4
#> 6 df.residual 1.860470323e+4
#> 7 nobs 1.863300000e+4
#> 8 adj.r.squared 8.089570581e-2
#> 9 npar 2.9 e+1
#>
#> ── Model D ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(57.883)
#> Link function: logit
#>
#> Formula:
#> beipr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -1.942409649 0.007664525 -253.42859 < 2.22e-16 ***
#> year.L 0.137213872 0.034119652 4.02155 0.000057817 ***
#> year.Q -0.037987379 0.028763563 -1.32068 0.186609
#> year.C 0.033125217 0.028548088 1.16033 0.245914
#> year^4 -0.031590691 0.025861863 -1.22152 0.221891
#> year^5 0.015382103 0.028377902 0.54205 0.587787
#> year^6 -0.057862065 0.025969076 -2.22811 0.025873 *
#> year^7 0.038112616 0.026103459 1.46006 0.144274
#> year^8 0.026938346 0.026120003 1.03133 0.302386
#> year^9 -0.004481966 0.028839435 -0.15541 0.876497
#> year^10 -0.002943281 0.027488097 -0.10707 0.914730
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 2.672467 3.419177 9.52419 0.031068 *
#> s(gdp_per_capita) 8.158620 8.794660 242.51498 < 2e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.123 Deviance explained = 12.4%
#> -REML = -4408.6 Scale est. = 1 n = 2538
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0.1232997714 weak cohen1988
#> 2 SE 0.01167507694 <NA> <NA>
#> 3 Lower CI 0.1004170411 weak cohen1988
#> 4 Upper CI 0.1461825018 moderate cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.183108776e+1
#> 2 logLik 4.467818979e+3
#> 3 AIC -8.887360976e+3
#> 4 BIC -8.746413152e+3
#> 5 deviance 2.480929226e+3
#> 6 df.residual 2.516168912e+3
#> 7 nobs 2.5380 e+3
#> 8 adj.r.squared 1.232997714e-1
#> 9 npar 2.9 e+1Code
beipr_gam_2_by_misfs |>
summarise_coefs_misfs() |>
md_named_tibble()beipr_gam_2_by_misfs model.
| A | B | C | D | |
|---|---|---|---|---|
| [Mean] | -0.0610390985 | -0.1005381217 | -0.2450296481 | -0.2522643755 |
| (Intercept) | -2.6627515887 | -2.8597345212 | -2.5116637422 | -1.9424096487 |
| year.L | 0.6580783368 | 0.3192435445 | 0.1236713781 | 0.1372138716 |
| year.Q | -0.1535903182 | -0.1348876475 | 0.0713469204 | -0.0379873788 |
| year.C | -0.0319602766 | -0.0417542439 | -0.0056971267 | 0.0331252168 |
| year^4 | 0.0429701806 | -0.0349092831 | -0.0237964900 | -0.0315906905 |
| year^5 | 0.0516161764 | 0.0647292959 | 0.0064209625 | 0.0153821031 |
| year^6 | -0.0986717683 | -0.0611552876 | -0.0918151146 | -0.0578620645 |
| year^7 | -0.0310435999 | 0.0219200593 | 0.0129203654 | 0.0381126159 |
| year^8 | 0.0491960520 | 0.0406306375 | 0.0682837874 | 0.0269383456 |
| year^9 | 0.0137200727 | -0.0526468777 | -0.0184534990 | -0.0044819657 |
| year^10 | 0.0241972313 | 0.0942613000 | 0.0412767425 | -0.0029432810 |
| mean(s(spei_12m)) | -0.0293562426 | -0.0123000663 | -0.0130620883 | -0.0157785180 |
| mean(s(gdp_per_capita)) | 0.0702568698 | -0.0178446565 | -0.5178661314 | -0.5941285946 |
Source: Created by the authors.
Code
data |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam_misfs(
gam_models = beipr_gam_2_by_misfs,
type = 2,
x_label = "Standardised Precipitation Evapotranspiration Index (12 months)",
y_label = "Predicted probability of BEIPR"
)beipr_gam_2_by_misfs model. All other variables are held constant at their mean values except SPEI. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
data |>
summarise_gam_misfs(mbepr_beipr_gam_2_by_misfs)
#>
#> ── Model A ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(18.267)
#> Link function: logit
#>
#> Formula:
#> mbepr_beipr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -1.939366580 0.007511323 -258.19242 < 2.22e-16 ***
#> year.L 0.468207179 0.037382429 12.52479 < 2.22e-16 ***
#> year.Q -0.173701269 0.027016624 -6.42942 0.00000000012809 ***
#> year.C 0.017294488 0.025649233 0.67427 0.50014017
#> year^4 0.023163104 0.026697128 0.86763 0.38559948
#> year^5 0.101654073 0.030324141 3.35225 0.00080158 ***
#> year^6 -0.112666955 0.028227765 -3.99135 0.00006569760936 ***
#> year^7 0.027145988 0.025436306 1.06721 0.28587511
#> year^8 0.025951564 0.025383126 1.02239 0.30659431
#> year^9 -0.049691189 0.026067108 -1.90628 0.05661397 .
#> year^10 -0.042523641 0.024631624 -1.72638 0.08427836 .
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 3.020606 3.879663 6.40391 0.2102
#> s(gdp_per_capita) 8.578943 8.946782 297.75208 <2e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0395 Deviance explained = 5.29%
#> -REML = -9222.2 Scale est. = 1 n = 7271
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 3.951783790e-2 weak cohen1988
#> 2 SE 4.284189687e-3 <NA> <NA>
#> 3 Lower CI 3.112098041e-2 weak cohen1988
#> 4 Upper CI 4.791469539e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.259954856e+1
#> 2 logLik 9.284757045e+3
#> 3 AIC -1.851986120e+4
#> 4 BIC -1.834876605e+4
#> 5 deviance 7.108154908e+3
#> 6 df.residual 7.248400451e+3
#> 7 nobs 7.271000000e+3
#> 8 adj.r.squared 3.951783790e-2
#> 9 npar 2.9 e+1
#>
#> ── Model B ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(16.995)
#> Link function: logit
#>
#> Formula:
#> mbepr_beipr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.213617891 0.004156974 -532.50707 < 2.22e-16 ***
#> year.L 0.193122378 0.018924770 10.20474 < 2.22e-16 ***
#> year.Q -0.164257222 0.014298655 -11.48760 < 2.22e-16 ***
#> year.C -0.008919064 0.013994962 -0.63731 0.52392598
#> year^4 -0.022453820 0.014270733 -1.57342 0.11562218
#> year^5 0.062069204 0.014687539 4.22598 0.0000237906 ***
#> year^6 -0.069054507 0.015485892 -4.45919 0.0000082271 ***
#> year^7 0.036450489 0.014271844 2.55401 0.01064890 *
#> year^8 0.036683084 0.014122623 2.59747 0.00939134 **
#> year^9 -0.054772410 0.014781325 -3.70551 0.00021096 ***
#> year^10 0.051849250 0.015089810 3.43604 0.00059028 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 4.541934 5.656737 34.66547 0.0000039428 ***
#> s(gdp_per_capita) 8.721479 8.974247 557.97287 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = -0.00315 Deviance explained = 2.67%
#> -REML = -40966 Scale est. = 1 n = 29045
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.426341372e+1
#> 2 logLik 4.104214771e+4
#> 3 AIC -8.203194150e+4
#> 4 BIC -8.181528527e+4
#> 5 deviance 2.915430259e+4
#> 6 df.residual 2.902073659e+4
#> 7 nobs 2.9045000 e+4
#> 8 adj.r.squared -3.151607063e-3
#> 9 npar 2.9 e+1
#>
#> ── Model C ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(34.171)
#> Link function: logit
#>
#> Formula:
#> mbepr_beipr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -1.788667558 0.003424242 -522.35430 < 2.22e-16 ***
#> year.L -0.009517005 0.025542439 -0.37260 0.7094493
#> year.Q 0.089321476 0.014228559 6.27762 0.0000000003438 ***
#> year.C 0.016778113 0.012736974 1.31728 0.1877460
#> year^4 -0.040804014 0.012726062 -3.20633 0.0013444 **
#> year^5 0.031141253 0.012949281 2.40486 0.0161785 *
#> year^6 -0.072499625 0.014512368 -4.99571 0.0000005861877 ***
#> year^7 0.026333031 0.012309170 2.13930 0.0324112 *
#> year^8 0.087796627 0.018033021 4.86866 0.0000011235815 ***
#> year^9 -0.050219673 0.014395458 -3.48858 0.0004856 ***
#> year^10 0.006297916 0.011821595 0.53275 0.5942089
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 8.562054 8.947813 97.68265 < 2.22e-16 ***
#> s(gdp_per_capita) 8.862406 8.994065 450.87895 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.075 Deviance explained = 6.43%
#> -REML = -27044 Scale est. = 1 n = 18633
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 7.500488523e-2 weak cohen1988
#> 2 SE 3.552974451e-3 <NA> <NA>
#> 3 Lower CI 6.804118327e-2 weak cohen1988
#> 4 Upper CI 8.196858719e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.842446036e+1
#> 2 logLik 2.713838974e+4
#> 3 AIC -5.421691429e+4
#> 4 BIC -5.398246154e+4
#> 5 deviance 1.817912696e+4
#> 6 df.residual 1.860457554e+4
#> 7 nobs 1.863300000e+4
#> 8 adj.r.squared 7.500488523e-2
#> 9 npar 2.9 e+1
#>
#> ── Model D ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(26.853)
#> Link function: logit
#>
#> Formula:
#> mbepr_beipr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -1.2772107657 0.0089833598 -142.17518 < 2.22e-16 ***
#> year.L 0.0119926417 0.0396178451 0.30271 0.7621123
#> year.Q 0.0111362275 0.0332661952 0.33476 0.7378053
#> year.C 0.0171028584 0.0326422174 0.52395 0.6003140
#> year^4 0.0003162651 0.0296378062 0.01067 0.9914859
#> year^5 0.0294287719 0.0326101164 0.90244 0.3668216
#> year^6 -0.0842882184 0.0301334206 -2.79717 0.0051553 **
#> year^7 0.0553810097 0.0301724780 1.83548 0.0664345 .
#> year^8 0.0665652652 0.0304665761 2.18486 0.0288990 *
#> year^9 -0.0524509891 0.0336971480 -1.55654 0.1195795
#> year^10 -0.0128174624 0.0300331402 -0.42678 0.6695415
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 1.004184 1.008355 0.80454 0.37076
#> s(gdp_per_capita) 8.074655 8.755006 230.86183 < 2e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.14 Deviance explained = 14.3%
#> -REML = -2894.9 Scale est. = 1 n = 2538
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0.1403277857 moderate cohen1988
#> 2 SE 0.01221327742 <NA> <NA>
#> 3 Lower CI 0.1163902018 weak cohen1988
#> 4 Upper CI 0.1642653696 moderate cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.007883926e+1
#> 2 logLik 2.949316369e+3
#> 3 AIC -5.855448281e+3
#> 4 BIC -5.729368413e+3
#> 5 deviance 2.457919422e+3
#> 6 df.residual 2.517921161e+3
#> 7 nobs 2.5380 e+3
#> 8 adj.r.squared 1.403277857e-1
#> 9 npar 2.9 e+1Code
mbepr_beipr_gam_2_by_misfs |>
summarise_coefs_misfs() |>
md_named_tibble()mbepr_beipr_gam_2_by_misfs model.
| A | B | C | D | |
|---|---|---|---|---|
| [Mean] | -0.0379331610 | -0.0809146803 | -0.2434751026 | -0.3098402383 |
| (Intercept) | -1.9393665796 | -2.2136178909 | -1.7886675584 | -1.2772107657 |
| year.L | 0.4682071788 | 0.1931223779 | -0.0095170045 | 0.0119926417 |
| year.Q | -0.1737012693 | -0.1642572218 | 0.0893214765 | 0.0111362275 |
| year.C | 0.0172944881 | -0.0089190640 | 0.0167781131 | 0.0171028584 |
| year^4 | 0.0231631039 | -0.0224538203 | -0.0408040144 | 0.0003162651 |
| year^5 | 0.1016540734 | 0.0620692037 | 0.0311412534 | 0.0294287719 |
| year^6 | -0.1126669550 | -0.0690545073 | -0.0724996255 | -0.0842882184 |
| year^7 | 0.0271459875 | 0.0364504888 | 0.0263330311 | 0.0553810097 |
| year^8 | 0.0259515636 | 0.0366830841 | 0.0877966272 | 0.0665652652 |
| year^9 | -0.0496911890 | -0.0547724104 | -0.0502196735 | -0.0524509891 |
| year^10 | -0.0425236414 | 0.0518492498 | 0.0062979157 | -0.0128174624 |
| mean(s(spei_12m)) | -0.0062429072 | 0.0214584160 | -0.0329240654 | 0.0013366481 |
| mean(s(gdp_per_capita)) | 0.0678508593 | -0.0429723293 | -0.5622691030 | -0.8625058164 |
Source: Created by the authors.
Code
data |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam_misfs(
gam_models = mbepr_beipr_gam_2_by_misfs,
type = 2,
x_label = "Standardised Precipitation Evapotranspiration Index (12 months)",
y_label = "Predicted probability of MBEPR & BEIPR"
)
#> Warning: Removed 500 rows containing missing values or values outside the scale range
#> (`geom_line()`).
#> Warning in max(ids, na.rm = TRUE): no non-missing arguments to max;
#> returning -Infmbepr_beipr_gam_2_by_misfs model. All other variables are held constant at their mean values except SPEI. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
data |>
summarise_gam_misfs(maper_gam_2_by_misfs)
#>
#> ── Model A ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(24.147)
#> Link function: logit
#>
#> Formula:
#> maper ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.54107555 0.01022405 -346.34761 < 2.22e-16 ***
#> year.L 0.19394939 0.05086947 3.81269 0.00013746 ***
#> year.Q -0.26225329 0.03687871 -7.11124 0.0000000000011501 ***
#> year.C -0.05752936 0.03494836 -1.64612 0.09973804 .
#> year^4 -0.05866581 0.03676100 -1.59587 0.11051761
#> year^5 -0.05720787 0.04352848 -1.31426 0.18875773
#> year^6 0.04818036 0.03927412 1.22677 0.21990854
#> year^7 0.03962575 0.03491759 1.13484 0.25644387
#> year^8 0.11637192 0.03464760 3.35873 0.00078302 ***
#> year^9 -0.06953381 0.03588885 -1.93748 0.05268708 .
#> year^10 -0.02489812 0.03397401 -0.73286 0.46364503
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 4.247119 5.365345 17.64906 0.0048491 **
#> s(gdp_per_capita) 6.755200 7.847116 54.04785 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = -0.0047 Deviance explained = 2.2%
#> -REML = -19070 Scale est. = 1 n = 7271
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.200231852e+1
#> 2 logLik 1.912192573e+4
#> 3 AIC -3.819342653e+4
#> 4 BIC -3.801967110e+4
#> 5 deviance 7.707238177e+3
#> 6 df.residual 7.248997681e+3
#> 7 nobs 7.271000000e+3
#> 8 adj.r.squared -4.700829275e-3
#> 9 npar 2.9 e+1
#>
#> ── Model B ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(24.738)
#> Link function: logit
#>
#> Formula:
#> maper ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.982412344 0.005425053 -734.07810 < 2.22e-16 ***
#> year.L 0.222808885 0.024817947 8.97773 < 2.22e-16 ***
#> year.Q -0.294794254 0.018815897 -15.66730 < 2.22e-16 ***
#> year.C -0.118169058 0.018224533 -6.48407 0.0000000000892836 ***
#> year^4 -0.068367888 0.018932097 -3.61122 0.00030476 ***
#> year^5 0.108388987 0.019334298 5.60605 0.0000000206999638 ***
#> year^6 -0.026461247 0.020551314 -1.28757 0.19789581
#> year^7 0.112840976 0.019240116 5.86488 0.0000000044945729 ***
#> year^8 0.091988899 0.018593875 4.94727 0.0000007526200916 ***
#> year^9 -0.099319882 0.019474071 -5.10011 0.0000003394583059 ***
#> year^10 0.139139088 0.020054271 6.93813 0.0000000000039733 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 8.556612 8.946522 321.4451 < 2.22e-16 ***
#> s(gdp_per_capita) 8.825283 8.989705 864.3839 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0134 Deviance explained = 4.75%
#> -REML = -96467 Scale est. = 1 n = 29045
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 1.338691524e-2 very weak (negligible) cohen1988
#> 2 SE 1.281384430e-3 <NA> <NA>
#> 3 Lower CI 1.087544791e-2 very weak (negligible) cohen1988
#> 4 Upper CI 1.589838258e-2 very weak (negligible) cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.838189508e+1
#> 2 logLik 9.655564883e+4
#> 3 AIC -1.930514252e+5
#> 4 BIC -1.928036550e+5
#> 5 deviance 3.127616722e+4
#> 6 df.residual 2.901661810e+4
#> 7 nobs 2.9045000 e+4
#> 8 adj.r.squared 1.338691524e-2
#> 9 npar 2.9 e+1
#>
#> ── Model C ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(53.919)
#> Link function: logit
#>
#> Formula:
#> maper ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.418964243 0.004931357 -693.31109 < 2.22e-16 ***
#> year.L -0.106646411 0.036004940 -2.96199 0.00305654 **
#> year.Q -0.125409731 0.020354656 -6.16123 0.000000000721818 ***
#> year.C 0.033149457 0.018281480 1.81328 0.06978851 .
#> year^4 -0.068833656 0.018317246 -3.75786 0.00017137 ***
#> year^5 0.122202158 0.018625444 6.56103 0.000000000053436 ***
#> year^6 0.022145551 0.020855409 1.06186 0.28829868
#> year^7 0.005444664 0.017579170 0.30972 0.75677203
#> year^8 0.117463911 0.025605619 4.58743 0.000004487421709 ***
#> year^9 -0.139077709 0.020277136 -6.85884 0.000000000006942 ***
#> year^10 0.030103417 0.016604375 1.81298 0.06983474 .
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 7.466508 8.445423 125.26600 < 2.22e-16 ***
#> s(gdp_per_capita) 8.170350 8.807415 94.89469 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0129 Deviance explained = 2.46%
#> -REML = -47148 Scale est. = 1 n = 18633
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 1.286151339e-2 very weak (negligible) cohen1988
#> 2 SE 1.570116912e-3 <NA> <NA>
#> 3 Lower CI 9.784140789e-3 very weak (negligible) cohen1988
#> 4 Upper CI 1.593888599e-2 very weak (negligible) cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.663685747e+1
#> 2 logLik 4.722342544e+4
#> 3 AIC -9.438884293e+4
#> 4 BIC -9.416166379e+4
#> 5 deviance 1.837359661e+4
#> 6 df.residual 1.860636314e+4
#> 7 nobs 1.863300000e+4
#> 8 adj.r.squared 1.286151339e-2
#> 9 npar 2.9 e+1
#>
#> ── Model D ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(90.209)
#> Link function: logit
#>
#> Formula:
#> maper ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.532521982 0.011436983 -308.86836 < 2.22e-16 ***
#> year.L -0.159253650 0.045477707 -3.50180 0.00046213 ***
#> year.Q -0.122596136 0.041408766 -2.96063 0.00307008 **
#> year.C -0.114564445 0.041546431 -2.75750 0.00582445 **
#> year^4 0.030453251 0.038149798 0.79825 0.42472277
#> year^5 0.088111864 0.041664991 2.11477 0.03444958 *
#> year^6 -0.008328661 0.038607134 -0.21573 0.82919935
#> year^7 0.096667184 0.038332450 2.52181 0.01167525 *
#> year^8 -0.006749917 0.038553545 -0.17508 0.86101755
#> year^9 -0.032654209 0.042197713 -0.77384 0.43902639
#> year^10 0.036410928 0.037573282 0.96906 0.33251308
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 1.011885 1.023682 0.58730 0.45441626
#> s(gdp_per_capita) 1.951469 2.408008 16.40875 0.00055587 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0234 Deviance explained = 3.33%
#> -REML = -6990.3 Scale est. = 1 n = 2538
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 2.339901231e-2 weak cohen1988
#> 2 SE 5.665567499e-3 <NA> <NA>
#> 3 Lower CI 1.229470406e-2 very weak (negligible) cohen1988
#> 4 Upper CI 3.450332056e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.396335330e+1
#> 2 logLik 7.025127363e+3
#> 3 AIC -1.401939135e+4
#> 4 BIC -1.392928368e+4
#> 5 deviance 2.476938563e+3
#> 6 df.residual 2.524036647e+3
#> 7 nobs 2.5380 e+3
#> 8 adj.r.squared 2.339901231e-2
#> 9 npar 2.9 e+1Code
maper_gam_2_by_misfs |>
summarise_coefs_misfs() |>
md_named_tibble()maper_gam_2_by_misfs model.
| A | B | C | D | |
|---|---|---|---|---|
| [Mean] | -0.1546098852 | -0.1910681006 | -0.1937536269 | -0.1421961029 |
| (Intercept) | -3.5410755525 | -3.9824123436 | -3.4189642434 | -3.5325219821 |
| year.L | 0.1939493869 | 0.2228088848 | -0.1066464112 | -0.1592536498 |
| year.Q | -0.2622532913 | -0.2947942537 | -0.1254097313 | -0.1225961365 |
| year.C | -0.0575293609 | -0.1181690583 | 0.0331494572 | -0.1145644448 |
| year^4 | -0.0586658142 | -0.0683678878 | -0.0688336556 | 0.0304532512 |
| year^5 | -0.0572078741 | 0.1083889875 | 0.1222021580 | 0.0881118637 |
| year^6 | 0.0481803627 | -0.0264612474 | 0.0221455508 | -0.0083286610 |
| year^7 | 0.0396257475 | 0.1128409758 | 0.0054446636 | 0.0966671844 |
| year^8 | 0.1163719194 | 0.0919888989 | 0.1174639105 | -0.0067499165 |
| year^9 | -0.0695338130 | -0.0993198816 | -0.1390777088 | -0.0326542091 |
| year^10 | -0.0248981238 | 0.1391390877 | 0.0301034168 | 0.0364109280 |
| mean(s(spei_12m)) | 0.0239209369 | -0.0457889341 | -0.0420129688 | 0.0015068309 |
| mean(s(gdp_per_capita)) | -0.1139931878 | -0.1349462968 | -0.1902573186 | -0.0458025210 |
Source: Created by the authors.
Code
data |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam_misfs(
gam_models = maper_gam_2_by_misfs,
type = 2,
x_label = "Standardised Precipitation Evapotranspiration Index (12 months)",
y_label = "Predicted probability of MAPER"
)maper_gam_2_by_misfs model. All other variables are held constant at their mean values except SPEI. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
data |>
summarise_gam_misfs(mpepr_gam_2_by_misfs)
#>
#> ── Model A ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(32.574)
#> Link function: logit
#>
#> Formula:
#> mpepr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.431305902 0.009298401 -369.02105 < 2.22e-16 ***
#> year.L 0.418079843 0.046935346 8.90757 < 2.22e-16 ***
#> year.Q -0.252878396 0.034066894 -7.42300 0.0000000000001145 ***
#> year.C -0.071600888 0.031907177 -2.24404 0.0248300 *
#> year^4 -0.100825588 0.033582783 -3.00230 0.0026795 **
#> year^5 -0.164835522 0.040304817 -4.08972 0.0000431889327845 ***
#> year^6 0.071949339 0.036133076 1.99123 0.0464554 *
#> year^7 -0.062788395 0.031699556 -1.98073 0.0476211 *
#> year^8 0.069605824 0.031909257 2.18137 0.0291562 *
#> year^9 -0.082450811 0.032788930 -2.51459 0.0119170 *
#> year^10 0.133889408 0.031315508 4.27550 0.0000190710043459 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 5.692085 6.957205 36.69025 < 2.22e-16 ***
#> s(gdp_per_capita) 8.181016 8.810878 117.03914 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = -0.0265 Deviance explained = 4.5%
#> -REML = -17923 Scale est. = 1 n = 7271
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.487310079e+1
#> 2 logLik 1.798487580e+4
#> 3 AIC -3.591421544e+4
#> 4 BIC -3.572284756e+4
#> 5 deviance 7.684990495e+3
#> 6 df.residual 7.246126899e+3
#> 7 nobs 7.271000000e+3
#> 8 adj.r.squared -2.648334231e-2
#> 9 npar 2.9 e+1
#>
#> ── Model B ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(27.853)
#> Link function: logit
#>
#> Formula:
#> mpepr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.768191002 0.005164089 -729.69132 < 2.22e-16 ***
#> year.L 0.375575251 0.023642786 15.88541 < 2.22e-16 ***
#> year.Q -0.159117052 0.017935146 -8.87180 < 2.22e-16 ***
#> year.C -0.145041679 0.017292361 -8.38762 < 2.22e-16 ***
#> year^4 -0.165049430 0.017994398 -9.17227 < 2.22e-16 ***
#> year^5 0.084651155 0.018383852 4.60465 0.0000041316533234 ***
#> year^6 0.042189879 0.019525566 2.16075 0.03071461 *
#> year^7 0.084183481 0.018268857 4.60803 0.0000040649773207 ***
#> year^8 0.079752657 0.017632727 4.52299 0.0000060972003636 ***
#> year^9 -0.069340864 0.018549111 -3.73823 0.00018532 ***
#> year^10 0.135114358 0.019235242 7.02431 0.0000000000021512 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 8.791883 8.987806 444.2199 < 2.22e-16 ***
#> s(gdp_per_capita) 8.839470 8.991264 932.8363 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.00813 Deviance explained = 5.93%
#> -REML = -84053 Scale est. = 1 n = 29045
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 8.132137454e-3 very weak (negligible) cohen1988
#> 2 SE 1.004034160e-3 <NA> <NA>
#> 3 Lower CI 6.164266661e-3 very weak (negligible) cohen1988
#> 4 Upper CI 1.010000825e-2 very weak (negligible) cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.863135285e+1
#> 2 logLik 8.414638145e+4
#> 3 AIC -1.682328048e+5
#> 4 BIC -1.679846799e+5
#> 5 deviance 3.189865427e+4
#> 6 df.residual 2.901636865e+4
#> 7 nobs 2.9045000 e+4
#> 8 adj.r.squared 8.132137454e-3
#> 9 npar 2.9 e+1
#>
#> ── Model C ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(93.143)
#> Link function: logit
#>
#> Formula:
#> mpepr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.34093609 0.00387263 -862.70473 < 2.22e-16 ***
#> year.L -0.09915093 0.02831758 -3.50139 0.00046284 ***
#> year.Q -0.07440449 0.01605759 -4.63360 0.0000035935712188 ***
#> year.C 0.09874149 0.01431219 6.89912 0.0000000000052326 ***
#> year^4 -0.12494085 0.01434959 -8.70693 < 2.22e-16 ***
#> year^5 0.05206759 0.01452172 3.58550 0.00033644 ***
#> year^6 -0.01687506 0.01626765 -1.03734 0.29957798
#> year^7 -0.06053119 0.01376364 -4.39791 0.0000109300157374 ***
#> year^8 0.13081017 0.01999001 6.54378 0.0000000000599837 ***
#> year^9 -0.09275571 0.01578003 -5.87804 0.0000000041514597 ***
#> year^10 0.01609911 0.01307274 1.23150 0.21813505
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 6.860406 8.000711 319.3766 < 2.22e-16 ***
#> s(gdp_per_capita) 8.480225 8.919608 254.3667 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0335 Deviance explained = 4.07%
#> -REML = -49540 Scale est. = 1 n = 18633
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 3.354566936e-2 weak cohen1988
#> 2 SE 2.482603924e-3 <NA> <NA>
#> 3 Lower CI 2.867985508e-2 weak cohen1988
#> 4 Upper CI 3.841148364e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.634063135e+1
#> 2 logLik 4.961835964e+4
#> 3 AIC -9.918011725e+4
#> 4 BIC -9.895844413e+4
#> 5 deviance 1.849066434e+4
#> 6 df.residual 1.860665937e+4
#> 7 nobs 1.863300000e+4
#> 8 adj.r.squared 3.354566936e-2
#> 9 npar 2.9 e+1
#>
#> ── Model D ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(118.894)
#> Link function: logit
#>
#> Formula:
#> mpepr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.323078644 0.009372166 -354.56890 < 2.22e-16 ***
#> year.L -0.031024498 0.038161049 -0.81299 0.41622459
#> year.Q -0.119358152 0.034027726 -3.50767 0.00045204 ***
#> year.C -0.034013954 0.034105490 -0.99732 0.31861110
#> year^4 0.035079463 0.031372405 1.11816 0.26349737
#> year^5 0.025803680 0.034067242 0.75743 0.44879002
#> year^6 -0.012785594 0.031589366 -0.40474 0.68566598
#> year^7 0.083565411 0.031587177 2.64555 0.00815586 **
#> year^8 -0.067300706 0.031657806 -2.12588 0.03351323 *
#> year^9 -0.002276603 0.034527589 -0.06594 0.94742897
#> year^10 0.010441924 0.030805977 0.33896 0.73464159
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 1.012723 1.025344 0.24008 0.6415545
#> s(gdp_per_capita) 2.940968 3.600515 13.47362 0.0067368 **
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.00808 Deviance explained = 2.01%
#> -REML = -6942.8 Scale est. = 1 n = 2538
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 8.080351296e-3 very weak (negligible) cohen1988
#> 2 SE 3.381575670e-3 <NA> <NA>
#> 3 Lower CI 1.452584770e-3 very weak (negligible) cohen1988
#> 4 Upper CI 1.470811782e-2 very weak (negligible) cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.495369067e+1
#> 2 logLik 6.982124166e+3
#> 3 AIC -1.393099661e+4
#> 4 BIC -1.383391603e+4
#> 5 deviance 2.488864184e+3
#> 6 df.residual 2.523046309e+3
#> 7 nobs 2.5380 e+3
#> 8 adj.r.squared 8.080351296e-3
#> 9 npar 2.9 e+1Code
mpepr_gam_2_by_misfs |>
summarise_coefs_misfs() |>
md_named_tibble()mpepr_gam_2_by_misfs model.
| A | B | C | D | |
|---|---|---|---|---|
| [Mean] | -0.0923921638 | -0.1865650987 | -0.1648796021 | -0.1265472223 |
| (Intercept) | -3.4313059020 | -3.7681910020 | -3.3409360850 | -3.3230786436 |
| year.L | 0.4180798434 | 0.3755752514 | -0.0991509332 | -0.0310244980 |
| year.Q | -0.2528783963 | -0.1591170523 | -0.0744044884 | -0.1193581517 |
| year.C | -0.0716008884 | -0.1450416788 | 0.0987414897 | -0.0340139544 |
| year^4 | -0.1008255885 | -0.1650494296 | -0.1249408540 | 0.0350794631 |
| year^5 | -0.1648355223 | 0.0846511545 | 0.0520675927 | 0.0258036801 |
| year^6 | 0.0719493387 | 0.0421898792 | -0.0168750641 | -0.0127855939 |
| year^7 | -0.0627883945 | 0.0841834813 | -0.0605311923 | 0.0835654106 |
| year^8 | 0.0696058242 | 0.0797526568 | 0.1308101666 | -0.0673007063 |
| year^9 | -0.0824508106 | -0.0693408642 | -0.0927557143 | -0.0022766030 |
| year^10 | 0.1338894080 | 0.1351143581 | 0.0160991117 | 0.0104419237 |
| mean(s(spei_12m)) | 0.0129178557 | -0.0604114187 | 0.0433028759 | 0.0008239560 |
| mean(s(gdp_per_capita)) | 0.0752808484 | -0.1512679831 | -0.1843731526 | -0.0269263754 |
Source: Created by the authors.
Code
data |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam_misfs(
gam_models = mpepr_gam_2_by_misfs,
type = 2,
x_label = "Standardised Precipitation Evapotranspiration Index (12 months)",
y_label = "Predicted probability of MPEPR"
)mpepr_gam_2_by_misfs model. All other variables are held constant at their mean values except SPEI. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
data |>
summarise_gam_misfs(maper_mpepr_gam_2_by_misfs)
#>
#> ── Model A ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(24.462)
#> Link function: logit
#>
#> Formula:
#> maper_mpepr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.751421488 0.008482062 -324.38120 < 2.22e-16 ***
#> year.L 0.140613699 0.042887617 3.27866 0.00104303 **
#> year.Q -0.258713202 0.031024430 -8.33902 < 2.22e-16 ***
#> year.C -0.048547358 0.029070782 -1.66997 0.09492514 .
#> year^4 -0.063029318 0.030659671 -2.05577 0.03980442 *
#> year^5 -0.132804208 0.036726124 -3.61607 0.00029911 ***
#> year^6 0.059888337 0.032886412 1.82107 0.06859677 .
#> year^7 -0.005492884 0.028995777 -0.18944 0.84975002
#> year^8 0.074475763 0.028854490 2.58108 0.00984916 **
#> year^9 -0.100155590 0.029761011 -3.36533 0.00076452 ***
#> year^10 0.044649069 0.028217284 1.58233 0.11357415
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 5.144458 6.380688 42.06683 0.0000021952 ***
#> s(gdp_per_capita) 8.054174 8.752707 120.17626 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.000893 Deviance explained = 3.91%
#> -REML = -13536 Scale est. = 1 n = 7271
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 8.926017278e-4 very weak (negligible) cohen1988
#> 2 SE 6.697671402e-4 <NA> <NA>
#> 3 Lower CI -4.201177451e-4 no effect cohen1988
#> 4 Upper CI 2.205321201e-3 very weak (negligible) cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.419863217e+1
#> 2 logLik 1.359742659e+4
#> 3 AIC -2.714159000e+4
#> 4 BIC -2.695805445e+4
#> 5 deviance 7.323591552e+3
#> 6 df.residual 7.246801368e+3
#> 7 nobs 7.271000000e+3
#> 8 adj.r.squared 8.926017278e-4
#> 9 npar 2.9 e+1
#>
#> ── Model B ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(19.87)
#> Link function: logit
#>
#> Formula:
#> maper_mpepr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.156638008 0.004963215 -636.00675 < 2.22e-16 ***
#> year.L 0.305884520 0.022772106 13.43242 < 2.22e-16 ***
#> year.Q -0.200975296 0.017235847 -11.66031 < 2.22e-16 ***
#> year.C -0.154736303 0.016618809 -9.31091 < 2.22e-16 ***
#> year^4 -0.144732230 0.017289239 -8.37123 < 2.22e-16 ***
#> year^5 0.098006122 0.017624583 5.56076 0.0000000268598336 ***
#> year^6 0.035838049 0.018720216 1.91440 0.0555686 .
#> year^7 0.122238053 0.017535428 6.97092 0.0000000000031488 ***
#> year^8 0.070956701 0.016906644 4.19697 0.0000270508039197 ***
#> year^9 -0.047726861 0.017782619 -2.68391 0.0072768 **
#> year^10 0.105711643 0.018439891 5.73277 0.0000000098803968 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 8.789591 8.987551 386.7282 < 2.22e-16 ***
#> s(gdp_per_capita) 8.864479 8.993765 1217.6427 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0226 Deviance explained = 6.54%
#> -REML = -64648 Scale est. = 1 n = 29045
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 2.264961359e-2 weak cohen1988
#> 2 SE 1.651098574e-3 <NA> <NA>
#> 3 Lower CI 1.941351985e-2 very weak (negligible) cohen1988
#> 4 Upper CI 2.588570733e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.865407015e+1
#> 2 logLik 6.474207706e+4
#> 3 AIC -1.294241915e+5
#> 4 BIC -1.291760481e+5
#> 5 deviance 3.098039438e+4
#> 6 df.residual 2.901634593e+4
#> 7 nobs 2.9045000 e+4
#> 8 adj.r.squared 2.264961359e-2
#> 9 npar 2.9 e+1
#>
#> ── Model C ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(50.006)
#> Link function: logit
#>
#> Formula:
#> maper_mpepr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.648976913 0.003885322 -681.79091 < 2.22e-16 ***
#> year.L -0.209289015 0.028253564 -7.40753 0.00000000000012868 ***
#> year.Q -0.054004039 0.016027023 -3.36956 0.00075288 ***
#> year.C 0.080799048 0.014361015 5.62628 0.00000001841404644 ***
#> year^4 -0.088698420 0.014396551 -6.16109 0.00000000072246747 ***
#> year^5 0.071023507 0.014627822 4.85537 0.00000120161392883 ***
#> year^6 0.002932272 0.016408428 0.17871 0.85816913
#> year^7 -0.008027666 0.013851600 -0.57955 0.56221951
#> year^8 0.130665903 0.020154919 6.48308 0.00000000008987028 ***
#> year^9 -0.096630240 0.015918564 -6.07029 0.00000000127682405 ***
#> year^10 0.017387835 0.013141087 1.32317 0.18578027
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 6.788722 7.942588 230.5865 < 2.22e-16 ***
#> s(gdp_per_capita) 8.177982 8.809404 179.1136 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0335 Deviance explained = 3.95%
#> -REML = -37767 Scale est. = 1 n = 18633
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 3.345831209e-2 weak cohen1988
#> 2 SE 2.479593414e-3 <NA> <NA>
#> 3 Lower CI 2.859839830e-2 weak cohen1988
#> 4 Upper CI 3.831822588e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.596670416e+1
#> 2 logLik 3.784267591e+4
#> 3 AIC -7.562915906e+4
#> 4 BIC -7.540908882e+4
#> 5 deviance 1.823334114e+4
#> 6 df.residual 1.860703330e+4
#> 7 nobs 1.863300000e+4
#> 8 adj.r.squared 3.345831209e-2
#> 9 npar 2.9 e+1
#>
#> ── Model D ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(63.388)
#> Link function: logit
#>
#> Formula:
#> maper_mpepr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.695624915 0.009663394 -278.95218 < 2.22e-16 ***
#> year.L -0.144663785 0.038661157 -3.74184 0.00018268 ***
#> year.Q -0.109716249 0.035001638 -3.13460 0.00172087 **
#> year.C -0.058524499 0.035097741 -1.66747 0.09542059 .
#> year^4 0.033064438 0.032320074 1.02303 0.30629319
#> year^5 0.040529387 0.035182040 1.15199 0.24932484
#> year^6 0.002498689 0.032613229 0.07662 0.93892918
#> year^7 0.101739705 0.032524857 3.12806 0.00175964 **
#> year^8 -0.049578296 0.032603892 -1.52063 0.12835395
#> year^9 -0.002859773 0.035600155 -0.08033 0.93597451
#> year^10 0.017620285 0.031846651 0.55329 0.58006806
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 1.025010 1.049637 0.19522 0.7018100
#> s(gdp_per_capita) 2.222026 2.728323 15.35648 0.0014765 **
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0244 Deviance explained = 3.22%
#> -REML = -5425.6 Scale est. = 1 n = 2538
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 2.435717666e-2 weak cohen1988
#> 2 SE 5.774731859e-3 <NA> <NA>
#> 3 Lower CI 1.303891020e-2 very weak (negligible) cohen1988
#> 4 Upper CI 3.567544313e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.424703656e+1
#> 2 logLik 5.463150490e+3
#> 3 AIC -1.089474506e+4
#> 4 BIC -1.080261548e+4
#> 5 deviance 2.479619569e+3
#> 6 df.residual 2.523752963e+3
#> 7 nobs 2.5380 e+3
#> 8 adj.r.squared 2.435717666e-2
#> 9 npar 2.9 e+1Code
maper_mpepr_gam_2_by_misfs |>
summarise_coefs_misfs() |>
md_named_tibble()maper_mpepr_gam_2_by_misfs model.
| A | B | C | D | |
|---|---|---|---|---|
| [Mean] | -0.1082130059 | -0.1657743707 | -0.1187755930 | -0.1102038959 |
| (Intercept) | -2.7514214879 | -3.1566380084 | -2.6489769132 | -2.6956249152 |
| year.L | 0.1406136994 | 0.3058845201 | -0.2092890147 | -0.1446637855 |
| year.Q | -0.2587132018 | -0.2009752963 | -0.0540040387 | -0.1097162486 |
| year.C | -0.0485473583 | -0.1547363029 | 0.0807990481 | -0.0585244992 |
| year^4 | -0.0630293175 | -0.1447322299 | -0.0886984201 | 0.0330644379 |
| year^5 | -0.1328042078 | 0.0980061220 | 0.0710235073 | 0.0405293873 |
| year^6 | 0.0598883373 | 0.0358380488 | 0.0029322725 | 0.0024986890 |
| year^7 | -0.0054928845 | 0.1222380534 | -0.0080276665 | 0.1017397050 |
| year^8 | 0.0744757633 | 0.0709567011 | 0.1306659029 | -0.0495782957 |
| year^9 | -0.1001555901 | -0.0477268614 | -0.0966302403 | -0.0028597734 |
| year^10 | 0.0446490686 | 0.1057116433 | 0.0173878355 | 0.0176202846 |
| mean(s(spei_12m)) | 0.0293925407 | -0.0365198205 | 0.0706258190 | 0.0008421603 |
| mean(s(gdp_per_capita)) | -0.0402414287 | -0.1680671949 | -0.1419229823 | -0.0375530457 |
Source: Created by the authors.
Code
data |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam_misfs(
gam_models = maper_mpepr_gam_2_by_misfs,
type = 2,
x_label = "Standardised Precipitation Evapotranspiration Index (12 months)",
y_label = "Predicted probability of MAPER & MPEPR"
)maper_mpepr_gam_2_by_misfs model. All other variables are held constant at their mean values except SPEI. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
By s(spei_12m) + s(gdp_per_capita) + year (Unordered year)
In this model, the year variable is treated as a unordered categorical variable.
dplyr::mutate(data, year = factor(year, ordered = FALSE)) |>
summarise_gam_misfs(mbepr_gam_3_by_misfs)
#>
#> ── Model A ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(19.243)
#> Link function: logit
#>
#> Formula:
#> mbepr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.29345758 0.03922414 -83.96506 < 2.22e-16 ***
#> year2009 0.38113814 0.05342253 7.13441 0.000000000000972045 ***
#> year2011 0.35746173 0.04725481 7.56456 0.000000000000038919 ***
#> year2012 0.37238373 0.05074703 7.33804 0.000000000000216743 ***
#> year2013 0.50683437 0.04828324 10.49711 < 2.22e-16 ***
#> year2014 0.70521400 0.05037534 13.99919 < 2.22e-16 ***
#> year2015 0.60565270 0.05561895 10.88932 < 2.22e-16 ***
#> year2016 0.71582038 0.05496072 13.02422 < 2.22e-16 ***
#> year2017 0.61438359 0.05381219 11.41718 < 2.22e-16 ***
#> year2018 0.65857556 0.05009520 13.14648 < 2.22e-16 ***
#> year2019 0.69408771 0.05751035 12.06892 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 4.213269 5.321403 19.62633 0.002229 **
#> s(gdp_per_capita) 7.983053 8.718735 136.86642 < 2e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = -0.0043 Deviance explained = 4.84%
#> -REML = -13462 Scale est. = 1 n = 7271
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.319632186e+1
#> 2 logLik 1.351835954e+4
#> 3 AIC -2.698515574e+4
#> 4 BIC -2.680747751e+4
#> 5 deviance 7.443829780e+3
#> 6 df.residual 7.247803678e+3
#> 7 nobs 7.271000000e+3
#> 8 adj.r.squared -4.304359701e-3
#> 9 npar 2.9 e+1
#>
#> ── Model B ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(17.174)
#> Link function: logit
#>
#> Formula:
#> mbepr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.40646962 0.01941116 -175.49028 < 2.22e-16 ***
#> year2009 0.24468411 0.02561504 9.55236 < 2.22e-16 ***
#> year2011 0.28923928 0.02516195 11.49511 < 2.22e-16 ***
#> year2012 0.21491095 0.02721915 7.89558 2.8897e-15 ***
#> year2013 0.44890949 0.02633677 17.04497 < 2.22e-16 ***
#> year2014 0.40767031 0.02749211 14.82863 < 2.22e-16 ***
#> year2015 0.41103172 0.02635930 15.59343 < 2.22e-16 ***
#> year2016 0.45424880 0.02694722 16.85698 < 2.22e-16 ***
#> year2017 0.42027043 0.02734804 15.36748 < 2.22e-16 ***
#> year2018 0.35013630 0.02744560 12.75746 < 2.22e-16 ***
#> year2019 0.28734467 0.02845582 10.09792 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 8.332668 8.882537 131.9754 < 2.22e-16 ***
#> s(gdp_per_capita) 8.666506 8.963381 511.9798 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = -0.00906 Deviance explained = 3.19%
#> -REML = -62821 Scale est. = 1 n = 29045
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.799917357e+1
#> 2 logLik 6.290498951e+4
#> 3 AIC -1.257502872e+5
#> 4 BIC -1.255032644e+5
#> 5 deviance 3.063357529e+4
#> 6 df.residual 2.901700083e+4
#> 7 nobs 2.9045000 e+4
#> 8 adj.r.squared -9.063547776e-3
#> 9 npar 2.9 e+1
#>
#> ── Model C ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(40.229)
#> Link function: logit
#>
#> Formula:
#> mbepr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.64148906 0.02070078 -127.60334 < 2.22e-16 ***
#> year2009 0.08282921 0.02019444 4.10158 0.000041033 ***
#> year2011 0.08781896 0.02237944 3.92409 0.000087058 ***
#> year2012 -0.07873481 0.03107743 -2.53351 0.0112928 *
#> year2013 0.02707531 0.02340528 1.15680 0.2473527
#> year2014 0.06469658 0.02262619 2.85937 0.0042449 **
#> year2015 -0.04840145 0.03241211 -1.49331 0.1353551
#> year2016 0.02474351 0.03559739 0.69509 0.4869967
#> year2017 0.03917031 0.03020185 1.29695 0.1946481
#> year2018 0.01373116 0.03120122 0.44008 0.6598763
#> year2019 0.04371550 0.03036720 1.43956 0.1499911
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 8.162494 8.819018 60.96357 < 2.22e-16 ***
#> s(gdp_per_capita) 8.797123 8.987155 235.09336 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.042 Deviance explained = 3.41%
#> -REML = -35899 Scale est. = 1 n = 18633
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 4.201543224e-2 weak cohen1988
#> 2 SE 2.754043533e-3 <NA> <NA>
#> 3 Lower CI 3.661760610e-2 weak cohen1988
#> 4 Upper CI 4.741325838e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.795961713e+1
#> 2 logLik 3.598537166e+4
#> 3 AIC -7.191113097e+4
#> 4 BIC -7.167766848e+4
#> 5 deviance 1.812816377e+4
#> 6 df.residual 1.860504038e+4
#> 7 nobs 1.863300000e+4
#> 8 adj.r.squared 4.201543224e-2
#> 9 npar 2.9 e+1
#>
#> ── Model D ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(37.383)
#> Link function: logit
#>
#> Formula:
#> mbepr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.248505937 0.039536102 -56.87222 < 2.22e-16 ***
#> year2009 0.047028126 0.047531960 0.98940 0.32246742
#> year2011 -0.020590121 0.049576514 -0.41532 0.67790761
#> year2012 -0.198631332 0.053589727 -3.70652 0.00021013 ***
#> year2013 0.004997577 0.051883154 0.09632 0.92326350
#> year2014 0.054019537 0.052618879 1.02662 0.30459994
#> year2015 -0.109909042 0.066994670 -1.64056 0.10088796
#> year2016 -0.052458382 0.058078911 -0.90323 0.36640596
#> year2017 -0.044906082 0.058305077 -0.77019 0.44118623
#> year2018 -0.065970079 0.056020835 -1.17760 0.23895651
#> year2019 -0.039197581 0.056050014 -0.69933 0.48434443
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 2.513916 3.221126 2.40512 0.45777
#> s(gdp_per_capita) 7.252433 8.226255 137.33956 < 2e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0877 Deviance explained = 10.8%
#> -REML = -4342.2 Scale est. = 1 n = 2538
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0.08772279128 weak cohen1988
#> 2 SE 0.01024732575 <NA> <NA>
#> 3 Lower CI 0.06763840187 weak cohen1988
#> 4 Upper CI 0.1078071807 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.076634920e+1
#> 2 logLik 4.391636743e+3
#> 3 AIC -8.736378724e+3
#> 4 BIC -8.599466376e+3
#> 5 deviance 2.448497468e+3
#> 6 df.residual 2.517233651e+3
#> 7 nobs 2.5380 e+3
#> 8 adj.r.squared 8.772279128e-2
#> 9 npar 2.9 e+1Code
mbepr_gam_3_by_misfs |>
summarise_coefs_misfs() |>
md_named_tibble()mbepr_gam_3_by_misfs model.
| A | B | C | D | |
|---|---|---|---|---|
| [Mean] | 0.0905257172 | -0.0093777689 | -0.2609963821 | -0.4083543833 |
| (Intercept) | -3.2934575847 | -3.4064696150 | -2.6414890643 | -2.2485059371 |
| year2009 | 0.3811381355 | 0.2446841146 | 0.0828292118 | 0.0470281261 |
| year2011 | 0.3574617319 | 0.2892392812 | 0.0878189626 | -0.0205901209 |
| year2012 | 0.3723837309 | 0.2149109514 | -0.0787348139 | -0.1986313325 |
| year2013 | 0.5068343694 | 0.4489094892 | 0.0270753076 | 0.0049975769 |
| year2014 | 0.7052140019 | 0.4076703076 | 0.0646965828 | 0.0540195366 |
| year2015 | 0.6056527010 | 0.4110317171 | -0.0484014469 | -0.1099090418 |
| year2016 | 0.7158203779 | 0.4542487981 | 0.0247435126 | -0.0524583824 |
| year2017 | 0.6143835928 | 0.4202704315 | 0.0391703135 | -0.0449060821 |
| year2018 | 0.6585755591 | 0.3501362974 | 0.0137311566 | -0.0659700791 |
| year2019 | 0.6940877056 | 0.2873446726 | 0.0437154960 | -0.0391975813 |
| mean(s(spei_12m)) | -0.0171356472 | 0.0117758792 | -0.0076226432 | 0.0017440117 |
| mean(s(gdp_per_capita)) | 0.0512635891 | -0.0555460728 | -0.5683829455 | -1.0204277669 |
Source: Created by the authors.
Code
dplyr::mutate(data, year = factor(year, ordered = FALSE)) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam_misfs(
gam_models = mbepr_gam_3_by_misfs,
type = 3,
x_label = "Standardised Precipitation Evapotranspiration Index (12 months)",
y_label = "Predicted probability of MBEPR"
)mbepr_gam_3_by_misfs model. All other variables are held constant at their mean values except SPEI. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
dplyr::mutate(data, year = factor(year, ordered = FALSE)) |>
summarise_gam_misfs(beipr_gam_3_by_misfs)
#>
#> ── Model A ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(26.645)
#> Link function: logit
#>
#> Formula:
#> beipr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.04798167 0.03402953 -89.56872 < 2.22e-16 ***
#> year2009 0.13518197 0.04750879 2.84541 0.0044354 **
#> year2011 0.18863165 0.04094500 4.60695 0.0000040861 ***
#> year2012 0.20610846 0.04459771 4.62150 0.0000038097 ***
#> year2013 0.35699013 0.04184809 8.53062 < 2.22e-16 ***
#> year2014 0.49687733 0.04435374 11.20260 < 2.22e-16 ***
#> year2015 0.56582338 0.04830311 11.71402 < 2.22e-16 ***
#> year2016 0.50102049 0.04808602 10.41925 < 2.22e-16 ***
#> year2017 0.55643782 0.04657743 11.94651 < 2.22e-16 ***
#> year2018 0.61166220 0.04318892 14.16248 < 2.22e-16 ***
#> year2019 0.61879741 0.04999682 12.37674 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 5.66093 6.914622 27.08158 0.00027339 ***
#> s(gdp_per_capita) 8.53392 8.934795 204.07291 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0241 Deviance explained = 5.81%
#> -REML = -13222 Scale est. = 1 n = 7271
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 2.413974465e-2 weak cohen1988
#> 2 SE 3.402019249e-3 <NA> <NA>
#> 3 Lower CI 1.747190945e-2 very weak (negligible) cohen1988
#> 4 Upper CI 3.080757986e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.519484923e+1
#> 2 logLik 1.328709678e+4
#> 3 AIC -2.651901920e+4
#> 4 BIC -2.632889805e+4
#> 5 deviance 7.384862076e+3
#> 6 df.residual 7.245805151e+3
#> 7 nobs 7.271000000e+3
#> 8 adj.r.squared 2.413974465e-2
#> 9 npar 2.9 e+1
#>
#> ── Model B ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(24.383)
#> Link function: logit
#>
#> Formula:
#> beipr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.09805733 0.01682532 -184.13068 < 2.22e-16 ***
#> year2009 0.14943122 0.02212487 6.75399 1.4383e-11 ***
#> year2011 0.17031529 0.02184206 7.79758 6.3104e-15 ***
#> year2012 0.08288759 0.02373244 3.49259 0.00047837 ***
#> year2013 0.29217259 0.02281434 12.80653 < 2.22e-16 ***
#> year2014 0.25707288 0.02389318 10.75926 < 2.22e-16 ***
#> year2015 0.34990851 0.02268679 15.42345 < 2.22e-16 ***
#> year2016 0.32542246 0.02334751 13.93821 < 2.22e-16 ***
#> year2017 0.36254999 0.02351630 15.41697 < 2.22e-16 ***
#> year2018 0.33248201 0.02360686 14.08413 < 2.22e-16 ***
#> year2019 0.29930832 0.02447886 12.22722 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 8.010772 8.752246 66.94599 < 2.22e-16 ***
#> s(gdp_per_capita) 8.679349 8.966034 524.44912 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = -0.0314 Deviance explained = 3.1%
#> -REML = -56534 Scale est. = 1 n = 29045
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.769012098e+1
#> 2 logLik 5.661758801e+4
#> 3 AIC -1.131757395e+5
#> 4 BIC -1.129297731e+5
#> 5 deviance 3.031701357e+4
#> 6 df.residual 2.901730988e+4
#> 7 nobs 2.9045000 e+4
#> 8 adj.r.squared -3.144979397e-2
#> 9 npar 2.9 e+1
#>
#> ── Model C ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(75.981)
#> Link function: logit
#>
#> Formula:
#> beipr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.553035101 0.015127773 -168.76477 < 2.22e-16 ***
#> year2009 0.050393419 0.014695108 3.42926 0.00060522 ***
#> year2011 0.018967042 0.016443732 1.15345 0.24872527
#> year2012 -0.078985998 0.022660015 -3.48570 0.00049085 ***
#> year2013 0.036571697 0.017127370 2.13528 0.03273831 *
#> year2014 0.048041803 0.016639147 2.88728 0.00388594 **
#> year2015 0.040607104 0.023562139 1.72340 0.08481534 .
#> year2016 -0.006481901 0.026076863 -0.24857 0.80369414
#> year2017 0.094639927 0.022056026 4.29089 0.0000177960405 ***
#> year2018 0.134071490 0.022668244 5.91451 0.0000000033287 ***
#> year2019 0.117260363 0.022172855 5.28846 0.0000001233472 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 8.397573 8.903406 65.41918 < 2.22e-16 ***
#> s(gdp_per_capita) 8.899197 8.996804 637.63411 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0809 Deviance explained = 6.05%
#> -REML = -39714 Scale est. = 1 n = 18633
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 8.089570581e-2 weak cohen1988
#> 2 SE 3.666362476e-3 <NA> <NA>
#> 3 Lower CI 7.370976740e-2 weak cohen1988
#> 4 Upper CI 8.808164422e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.829676986e+1
#> 2 logLik 3.980828045e+4
#> 3 AIC -7.955676047e+4
#> 4 BIC -7.932256141e+4
#> 5 deviance 1.836583071e+4
#> 6 df.residual 1.860470323e+4
#> 7 nobs 1.863300000e+4
#> 8 adj.r.squared 8.089570581e-2
#> 9 npar 2.9 e+1
#>
#> ── Model D ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(57.883)
#> Link function: logit
#>
#> Formula:
#> beipr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.06742282 0.03026461 -68.31155 < 2.22e-16 ***
#> year2009 0.11996293 0.03593504 3.33833 0.00084284 ***
#> year2011 0.08959779 0.03733718 2.39969 0.01640880 *
#> year2012 0.08415744 0.03959051 2.12570 0.03352846 *
#> year2013 0.13832694 0.03905920 3.54147 0.00039791 ***
#> year2014 0.16178969 0.03999674 4.04507 0.000052307 ***
#> year2015 0.12575730 0.04955894 2.53753 0.01116377 *
#> year2016 0.12525397 0.04355841 2.87554 0.00403336 **
#> year2017 0.17699950 0.04349766 4.06917 0.000047180 ***
#> year2018 0.17936211 0.04172591 4.29858 0.000017190 ***
#> year2019 0.17393720 0.04184036 4.15716 0.000032222 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 2.672467 3.419177 9.52419 0.031068 *
#> s(gdp_per_capita) 8.158620 8.794660 242.51498 < 2e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.123 Deviance explained = 12.4%
#> -REML = -4409.8 Scale est. = 1 n = 2538
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0.1232997714 weak cohen1988
#> 2 SE 0.01167507694 <NA> <NA>
#> 3 Lower CI 0.1004170411 weak cohen1988
#> 4 Upper CI 0.1461825018 moderate cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.183108776e+1
#> 2 logLik 4.467818979e+3
#> 3 AIC -8.887360976e+3
#> 4 BIC -8.746413152e+3
#> 5 deviance 2.480929226e+3
#> 6 df.residual 2.516168912e+3
#> 7 nobs 2.5380 e+3
#> 8 adj.r.squared 1.232997714e-1
#> 9 npar 2.9 e+1Code
beipr_gam_3_by_misfs |>
summarise_coefs_misfs() |>
md_named_tibble()beipr_gam_3_by_misfs model.
| A | B | C | D | |
|---|---|---|---|---|
| [Mean] | 0.0537122356 | -0.0257865164 | -0.2371139357 | -0.2131531711 |
| (Intercept) | -3.0479816664 | -3.0980573264 | -2.5530351008 | -2.0674228187 |
| year2009 | 0.1351819734 | 0.1494312161 | 0.0503934191 | 0.1199629338 |
| year2011 | 0.1886316495 | 0.1703152947 | 0.0189670417 | 0.0895977917 |
| year2012 | 0.2061084562 | 0.0828875885 | -0.0789859985 | 0.0841574435 |
| year2013 | 0.3569901304 | 0.2921725898 | 0.0365716968 | 0.1383269374 |
| year2014 | 0.4968773350 | 0.2570728777 | 0.0480418034 | 0.1617896934 |
| year2015 | 0.5658233800 | 0.3499085053 | 0.0406071037 | 0.1257572978 |
| year2016 | 0.5010204916 | 0.3254224613 | -0.0064819013 | 0.1252539673 |
| year2017 | 0.5564378243 | 0.3625499895 | 0.0946399265 | 0.1769994953 |
| year2018 | 0.6116622015 | 0.3324820125 | 0.1340714900 | 0.1793621065 |
| year2019 | 0.6187974134 | 0.2993083222 | 0.1172603633 | 0.1739372033 |
| mean(s(spei_12m)) | -0.0293562426 | -0.0123000663 | -0.0130620883 | -0.0157785180 |
| mean(s(gdp_per_capita)) | 0.0702568698 | -0.0178446565 | -0.5178661314 | -0.5941285946 |
Source: Created by the authors.
Code
dplyr::mutate(data, year = factor(year, ordered = FALSE)) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam_misfs(
gam_models = beipr_gam_3_by_misfs,
type = 3,
x_label = "Standardised Precipitation Evapotranspiration Index (12 months)",
y_label = "Predicted probability of BEIPR"
)beipr_gam_3_by_misfs model. All other variables are held constant at their mean values except SPEI. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
dplyr::mutate(data, year = factor(year, ordered = FALSE)) |>
summarise_gam_misfs(mbepr_beipr_gam_3_by_misfs)
#>
#> ── Model A ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(18.267)
#> Link function: logit
#>
#> Formula:
#> mbepr_beipr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.29235563 0.03104452 -73.84091 < 2.22e-16 ***
#> year2009 0.23312765 0.04148229 5.61993 0.000000019103 ***
#> year2011 0.20767734 0.03786622 5.48450 0.000000041464 ***
#> year2012 0.21089874 0.04033501 5.22868 0.000000170728 ***
#> year2013 0.36018712 0.03871929 9.30252 < 2.22e-16 ***
#> year2014 0.49900523 0.04013031 12.43462 < 2.22e-16 ***
#> year2015 0.44305785 0.04418189 10.02804 < 2.22e-16 ***
#> year2016 0.48924911 0.04440188 11.01866 < 2.22e-16 ***
#> year2017 0.44611570 0.04304649 10.36358 < 2.22e-16 ***
#> year2018 0.47958171 0.04024774 11.91574 < 2.22e-16 ***
#> year2019 0.51397910 0.04592658 11.19132 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 3.020606 3.879663 6.40391 0.2102
#> s(gdp_per_capita) 8.578943 8.946782 297.75208 <2e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0395 Deviance explained = 5.29%
#> -REML = -9223.4 Scale est. = 1 n = 7271
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 3.951783790e-2 weak cohen1988
#> 2 SE 4.284189687e-3 <NA> <NA>
#> 3 Lower CI 3.112098041e-2 weak cohen1988
#> 4 Upper CI 4.791469539e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.259954856e+1
#> 2 logLik 9.284757045e+3
#> 3 AIC -1.851986120e+4
#> 4 BIC -1.834876605e+4
#> 5 deviance 7.108154908e+3
#> 6 df.residual 7.248400451e+3
#> 7 nobs 7.271000000e+3
#> 8 adj.r.squared 3.951783790e-2
#> 9 npar 2.9 e+1
#>
#> ── Model B ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(16.995)
#> Link function: logit
#>
#> Formula:
#> mbepr_beipr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.41919358 0.01581646 -152.95418 < 2.22e-16 ***
#> year2009 0.16600899 0.02069811 8.02049 1.0532e-15 ***
#> year2011 0.16639740 0.02043914 8.14112 3.9165e-16 ***
#> year2012 0.10201898 0.02218430 4.59870 4.2513e-06 ***
#> year2013 0.27854034 0.02121132 13.13169 < 2.22e-16 ***
#> year2014 0.26494308 0.02243277 11.81054 < 2.22e-16 ***
#> year2015 0.28300496 0.02145058 13.19335 < 2.22e-16 ***
#> year2016 0.27292453 0.02202014 12.39431 < 2.22e-16 ***
#> year2017 0.27743869 0.02209579 12.55618 < 2.22e-16 ***
#> year2018 0.24015736 0.02236224 10.73942 < 2.22e-16 ***
#> year2019 0.20989831 0.02324140 9.03123 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 4.541934 5.656737 34.66547 0.0000039428 ***
#> s(gdp_per_capita) 8.721479 8.974247 557.97287 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = -0.00315 Deviance explained = 2.67%
#> -REML = -40967 Scale est. = 1 n = 29045
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.426341372e+1
#> 2 logLik 4.104214771e+4
#> 3 AIC -8.203194150e+4
#> 4 BIC -8.181528527e+4
#> 5 deviance 2.915430259e+4
#> 6 df.residual 2.902073659e+4
#> 7 nobs 2.9045000 e+4
#> 8 adj.r.squared -3.151607063e-3
#> 9 npar 2.9 e+1
#>
#> ── Model C ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(34.171)
#> Link function: logit
#>
#> Formula:
#> mbepr_beipr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -1.776999064 0.016794151 -105.81059 < 2.22e-16 ***
#> year2009 0.062037880 0.016339155 3.79688 0.00014653 ***
#> year2011 0.031590847 0.018196008 1.73614 0.08253879 .
#> year2012 -0.116126253 0.025242904 -4.60035 0.0000042178 ***
#> year2013 -0.018446502 0.019027690 -0.96946 0.33231790
#> year2014 0.004331179 0.018430087 0.23501 0.81420417
#> year2015 -0.071415086 0.026328487 -2.71246 0.00667849 **
#> year2016 -0.064213296 0.029041455 -2.21109 0.02702955 *
#> year2017 0.007313002 0.024577439 0.29755 0.76604710
#> year2018 0.012561430 0.025333030 0.49585 0.61999894
#> year2019 0.024013364 0.024714643 0.97162 0.33123715
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 8.562054 8.947813 97.68265 < 2.22e-16 ***
#> s(gdp_per_capita) 8.862406 8.994065 450.87895 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.075 Deviance explained = 6.43%
#> -REML = -27045 Scale est. = 1 n = 18633
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 7.500488523e-2 weak cohen1988
#> 2 SE 3.552974451e-3 <NA> <NA>
#> 3 Lower CI 6.804118327e-2 weak cohen1988
#> 4 Upper CI 8.196858719e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.842446036e+1
#> 2 logLik 2.713838974e+4
#> 3 AIC -5.421691429e+4
#> 4 BIC -5.398246154e+4
#> 5 deviance 1.817912696e+4
#> 6 df.residual 1.860457554e+4
#> 7 nobs 1.863300000e+4
#> 8 adj.r.squared 7.500488523e-2
#> 9 npar 2.9 e+1
#>
#> ── Model D ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(26.853)
#> Link function: logit
#>
#> Formula:
#> mbepr_beipr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -1.305401262 0.034500623 -37.83704 < 2e-16 ***
#> year2009 0.081476602 0.041222338 1.97652 0.048096 *
#> year2011 0.025581466 0.042858068 0.59689 0.550582
#> year2012 -0.056286936 0.045254417 -1.24379 0.213577
#> year2013 0.060142841 0.044776712 1.34317 0.179216
#> year2014 0.092113337 0.045530858 2.02310 0.043063 *
#> year2015 -0.015189444 0.056254145 -0.27001 0.787149
#> year2016 0.003010431 0.050388684 0.05974 0.952359
#> year2017 0.039937892 0.050205214 0.79549 0.426327
#> year2018 0.031191788 0.047809102 0.65242 0.514128
#> year2019 0.048117484 0.048194904 0.99839 0.318089
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 1.004184 1.008355 0.80454 0.37076
#> s(gdp_per_capita) 8.074655 8.755006 230.86183 < 2e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.14 Deviance explained = 14.3%
#> -REML = -2896.1 Scale est. = 1 n = 2538
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0.1403277857 moderate cohen1988
#> 2 SE 0.01221327742 <NA> <NA>
#> 3 Lower CI 0.1163902018 weak cohen1988
#> 4 Upper CI 0.1642653696 moderate cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.007883926e+1
#> 2 logLik 2.949316369e+3
#> 3 AIC -5.855448281e+3
#> 4 BIC -5.729368413e+3
#> 5 deviance 2.457919422e+3
#> 6 df.residual 2.517921161e+3
#> 7 nobs 2.5380 e+3
#> 8 adj.r.squared 1.403277857e-1
#> 9 npar 2.9 e+1Code
mbepr_beipr_gam_3_by_misfs |>
summarise_coefs_misfs() |>
md_named_tibble()mbepr_beipr_gam_3_by_misfs model.
| A | B | C | D | |
|---|---|---|---|---|
| [Mean] | 0.0739653619 | -0.0121202132 | -0.2504169315 | -0.3015802868 |
| (Intercept) | -2.2923556303 | -2.4191935836 | -1.7769990643 | -1.3054012621 |
| year2009 | 0.2331276473 | 0.1660089899 | 0.0620378802 | 0.0814766022 |
| year2011 | 0.2076773433 | 0.1663973962 | 0.0315908471 | 0.0255814665 |
| year2012 | 0.2108987360 | 0.1020189776 | -0.1161262530 | -0.0562869365 |
| year2013 | 0.3601871216 | 0.2785403398 | -0.0184465017 | 0.0601428407 |
| year2014 | 0.4990052338 | 0.2649430810 | 0.0043311789 | 0.0921133370 |
| year2015 | 0.4430578502 | 0.2830049579 | -0.0714150856 | -0.0151894441 |
| year2016 | 0.4892491119 | 0.2729245276 | -0.0642132964 | 0.0030104307 |
| year2017 | 0.4461156994 | 0.2774386859 | 0.0073130022 | 0.0399378920 |
| year2018 | 0.4795817133 | 0.2401573563 | 0.0125614299 | 0.0311917877 |
| year2019 | 0.5139791013 | 0.2098983069 | 0.0240133642 | 0.0481174839 |
| mean(s(spei_12m)) | -0.0062429072 | 0.0214584160 | -0.0329240654 | 0.0013366481 |
| mean(s(gdp_per_capita)) | 0.0678508593 | -0.0429723293 | -0.5622691030 | -0.8625058164 |
Source: Created by the authors.
Code
dplyr::mutate(data, year = factor(year, ordered = FALSE)) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam_misfs(
gam_models = mbepr_beipr_gam_3_by_misfs,
type = 3,
x_label = "Standardised Precipitation Evapotranspiration Index (12 months)",
y_label = "Predicted probability of MBEPR & BEIPR"
)
#> Warning: Removed 500 rows containing missing values or values outside the scale range
#> (`geom_line()`).
#> Warning in max(ids, na.rm = TRUE): no non-missing arguments to max;
#> returning -Infmbepr_beipr_gam_3_by_misfs model. All other variables are held constant at their mean values except SPEI. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
dplyr::mutate(data, year = factor(year, ordered = FALSE)) |>
summarise_gam_misfs(maper_gam_3_by_misfs)
#>
#> ── Model A ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(24.147)
#> Link function: logit
#>
#> Formula:
#> maper ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.74039932 0.04165768 -89.78895 < 2.22e-16 ***
#> year2009 0.02398721 0.05892763 0.40706 0.68396228
#> year2011 0.21211725 0.05060029 4.19202 0.00002764858817 ***
#> year2012 0.16025454 0.05445346 2.94296 0.00325087 **
#> year2013 0.27157993 0.05195628 5.22709 0.00000017220247 ***
#> year2014 0.31386443 0.05488656 5.71842 0.00000001075189 ***
#> year2015 0.20545993 0.06051133 3.39540 0.00068529 ***
#> year2016 0.30340505 0.06015133 5.04403 0.00000045582973 ***
#> year2017 0.37030847 0.05800356 6.38424 0.00000000017225 ***
#> year2018 0.22257044 0.05468459 4.07008 0.00004699785931 ***
#> year2019 0.10901415 0.06332311 1.72155 0.08515037 .
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 4.247119 5.365345 17.64906 0.0048491 **
#> s(gdp_per_capita) 6.755200 7.847116 54.04785 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = -0.0047 Deviance explained = 2.2%
#> -REML = -19071 Scale est. = 1 n = 7271
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.200231852e+1
#> 2 logLik 1.912192573e+4
#> 3 AIC -3.819342653e+4
#> 4 BIC -3.801967110e+4
#> 5 deviance 7.707238177e+3
#> 6 df.residual 7.248997681e+3
#> 7 nobs 7.271000000e+3
#> 8 adj.r.squared -4.700829275e-3
#> 9 npar 2.9 e+1
#>
#> ── Model B ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(24.738)
#> Link function: logit
#>
#> Formula:
#> maper ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -4.24347684 0.02041622 -207.84830 < 2.22e-16 ***
#> year2009 0.20182041 0.02717591 7.42644 1.1156e-13 ***
#> year2011 0.22249104 0.02667319 8.34137 < 2.22e-16 ***
#> year2012 0.07590031 0.02889485 2.62678 0.0086198 **
#> year2013 0.40503377 0.02804011 14.44480 < 2.22e-16 ***
#> year2014 0.30493334 0.02934774 10.39035 < 2.22e-16 ***
#> year2015 0.39223348 0.02798290 14.01690 < 2.22e-16 ***
#> year2016 0.40350972 0.02862591 14.09596 < 2.22e-16 ***
#> year2017 0.46440125 0.02890814 16.06472 < 2.22e-16 ***
#> year2018 0.23095878 0.02920618 7.90787 2.6182e-15 ***
#> year2019 0.17042732 0.03024568 5.63477 1.7530e-08 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 8.556612 8.946522 321.4451 < 2.22e-16 ***
#> s(gdp_per_capita) 8.825283 8.989705 864.3839 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0134 Deviance explained = 4.75%
#> -REML = -96468 Scale est. = 1 n = 29045
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 1.338691524e-2 very weak (negligible) cohen1988
#> 2 SE 1.281384430e-3 <NA> <NA>
#> 3 Lower CI 1.087544791e-2 very weak (negligible) cohen1988
#> 4 Upper CI 1.589838258e-2 very weak (negligible) cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.838189508e+1
#> 2 logLik 9.655564883e+4
#> 3 AIC -1.930514252e+5
#> 4 BIC -1.928036550e+5
#> 5 deviance 3.127616722e+4
#> 6 df.residual 2.901661810e+4
#> 7 nobs 2.9045000 e+4
#> 8 adj.r.squared 1.338691524e-2
#> 9 npar 2.9 e+1
#>
#> ── Model C ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(53.919)
#> Link function: logit
#>
#> Formula:
#> maper ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.49351141 0.02422530 -144.20920 < 2.22e-16 ***
#> year2009 0.13337997 0.02438097 5.47066 0.000000044837 ***
#> year2011 0.25141284 0.02635422 9.53975 < 2.22e-16 ***
#> year2012 -0.01973082 0.03618490 -0.54528 0.5855625
#> year2013 0.13856098 0.02706414 5.11973 0.000000305981 ***
#> year2014 0.11681197 0.02638188 4.42773 0.000009522788 ***
#> year2015 0.05948081 0.03744573 1.58845 0.1121838
#> year2016 0.12967045 0.04119403 3.14780 0.0016451 **
#> year2017 0.07755906 0.03497282 2.21770 0.0265756 *
#> year2018 -0.05247397 0.03638916 -1.44202 0.1492962
#> year2019 -0.01465246 0.03536640 -0.41430 0.6786511
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 7.466508 8.445423 125.26600 < 2.22e-16 ***
#> s(gdp_per_capita) 8.170350 8.807415 94.89469 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0129 Deviance explained = 2.46%
#> -REML = -47149 Scale est. = 1 n = 18633
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 1.286151339e-2 very weak (negligible) cohen1988
#> 2 SE 1.570116912e-3 <NA> <NA>
#> 3 Lower CI 9.784140789e-3 very weak (negligible) cohen1988
#> 4 Upper CI 1.593888599e-2 very weak (negligible) cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.663685747e+1
#> 2 logLik 4.722342544e+4
#> 3 AIC -9.438884293e+4
#> 4 BIC -9.416166379e+4
#> 5 deviance 1.837359661e+4
#> 6 df.residual 1.860636314e+4
#> 7 nobs 1.863300000e+4
#> 8 adj.r.squared 1.286151339e-2
#> 9 npar 2.9 e+1
#>
#> ── Model D ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(90.209)
#> Link function: logit
#>
#> Formula:
#> maper ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.485166840 0.040858133 -85.29922 < 2.22e-16 ***
#> year2009 0.042731334 0.052954427 0.80695 0.41969792
#> year2011 -0.078113844 0.053722540 -1.45402 0.14593975
#> year2012 -0.085456892 0.055976615 -1.52665 0.12684721
#> year2013 0.032025743 0.053001905 0.60424 0.54568570
#> year2014 -0.015765258 0.054350306 -0.29007 0.77176459
#> year2015 0.001618113 0.068687645 0.02356 0.98120553
#> year2016 0.016947152 0.059785064 0.28347 0.77681811
#> year2017 -0.032749850 0.059882160 -0.54690 0.58444404
#> year2018 -0.200881815 0.057531262 -3.49170 0.00047996 ***
#> year2019 -0.201261243 0.058124978 -3.46256 0.00053506 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 1.011885 1.023682 0.58730 0.45441626
#> s(gdp_per_capita) 1.951469 2.408008 16.40875 0.00055587 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0234 Deviance explained = 3.33%
#> -REML = -6991.5 Scale est. = 1 n = 2538
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 2.339901231e-2 weak cohen1988
#> 2 SE 5.665567499e-3 <NA> <NA>
#> 3 Lower CI 1.229470406e-2 very weak (negligible) cohen1988
#> 4 Upper CI 3.450332056e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.396335330e+1
#> 2 logLik 7.025127363e+3
#> 3 AIC -1.401939135e+4
#> 4 BIC -1.392928368e+4
#> 5 deviance 2.476938563e+3
#> 6 df.residual 2.524036647e+3
#> 7 nobs 2.5380 e+3
#> 8 adj.r.squared 2.339901231e-2
#> 9 npar 2.9 e+1Code
maper_gam_3_by_misfs |>
summarise_coefs_misfs() |>
md_named_tibble()maper_gam_3_by_misfs model.
| A | B | C | D | |
|---|---|---|---|---|
| [Mean] | -0.0813271779 | -0.1033925680 | -0.1642732816 | -0.1518874004 |
| (Intercept) | -3.7403993178 | -4.2434768385 | -3.4935114096 | -3.4851668401 |
| year2009 | 0.0239872119 | 0.2018204090 | 0.1333799698 | 0.0427313337 |
| year2011 | 0.2121172544 | 0.2224910373 | 0.2514128359 | -0.0781138444 |
| year2012 | 0.1602545443 | 0.0759003111 | -0.0197308203 | -0.0854568924 |
| year2013 | 0.2715799305 | 0.4050337725 | 0.1385609787 | 0.0320257434 |
| year2014 | 0.3138644343 | 0.3049333447 | 0.1168119692 | -0.0157652583 |
| year2015 | 0.2054599275 | 0.3922334850 | 0.0594808142 | 0.0016181130 |
| year2016 | 0.3034050520 | 0.4035097247 | 0.1296704486 | 0.0169471520 |
| year2017 | 0.3703084741 | 0.4644012545 | 0.0775590584 | -0.0327498495 |
| year2018 | 0.2225704396 | 0.2309587818 | -0.0524739697 | -0.2008818153 |
| year2019 | 0.1090141496 | 0.1704273232 | -0.0146524559 | -0.2012612435 |
| mean(s(spei_12m)) | 0.0239209369 | -0.0457889341 | -0.0420129688 | 0.0015068309 |
| mean(s(gdp_per_capita)) | -0.1139931878 | -0.1349462968 | -0.1902573186 | -0.0458025210 |
Source: Created by the authors.
Code
dplyr::mutate(data, year = factor(year, ordered = FALSE)) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam_misfs(
gam_models = maper_gam_3_by_misfs,
type = 3,
x_label = "Standardised Precipitation Evapotranspiration Index (12 months)",
y_label = "Predicted probability of MAPER"
)maper_gam_3_by_misfs model. All other variables are held constant at their mean values except SPEI. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
dplyr::mutate(data, year = factor(year, ordered = FALSE)) |>
summarise_gam_misfs(mpepr_gam_3_by_misfs)
#>
#> ── Model A ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(32.574)
#> Link function: logit
#>
#> Formula:
#> mpepr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.70554856 0.03914823 -94.65431 < 2.22e-16 ***
#> year2009 -0.06318694 0.05564683 -1.13550 0.25616618
#> year2011 0.27864614 0.04681438 5.95215 2.6465e-09 ***
#> year2012 0.19634912 0.05099548 3.85032 0.00011796 ***
#> year2013 0.38697026 0.04800738 8.06064 7.5896e-16 ***
#> year2014 0.24869584 0.05195238 4.78700 1.6930e-06 ***
#> year2015 0.37191656 0.05587458 6.65627 2.8086e-11 ***
#> year2016 0.38437547 0.05560340 6.91280 4.7516e-12 ***
#> year2017 0.48773249 0.05369215 9.08387 < 2.22e-16 ***
#> year2018 0.48199872 0.05025203 9.59163 < 2.22e-16 ***
#> year2019 0.24317155 0.05866329 4.14521 3.3951e-05 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 5.692085 6.957205 36.69025 < 2.22e-16 ***
#> s(gdp_per_capita) 8.181016 8.810878 117.03914 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = -0.0265 Deviance explained = 4.5%
#> -REML = -17924 Scale est. = 1 n = 7271
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.487310079e+1
#> 2 logLik 1.798487580e+4
#> 3 AIC -3.591421544e+4
#> 4 BIC -3.572284756e+4
#> 5 deviance 7.684990495e+3
#> 6 df.residual 7.246126899e+3
#> 7 nobs 7.271000000e+3
#> 8 adj.r.squared -2.648334231e-2
#> 9 npar 2.9 e+1
#>
#> ── Model B ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(27.853)
#> Link function: logit
#>
#> Formula:
#> mpepr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -4.03780407 0.01959620 -206.05034 < 2.22e-16 ***
#> year2009 0.16459906 0.02599572 6.33177 0.00000000024235678 ***
#> year2011 0.22439434 0.02553096 8.78911 < 2.22e-16 ***
#> year2012 0.07468282 0.02769766 2.69636 0.0070102 **
#> year2013 0.30333907 0.02695257 11.25455 < 2.22e-16 ***
#> year2014 0.20409976 0.02819042 7.24004 0.00000000000044856 ***
#> year2015 0.36450633 0.02677059 13.61592 < 2.22e-16 ***
#> year2016 0.43668211 0.02728135 16.00661 < 2.22e-16 ***
#> year2017 0.56484372 0.02738349 20.62717 < 2.22e-16 ***
#> year2018 0.35203426 0.02776343 12.67978 < 2.22e-16 ***
#> year2019 0.27656233 0.02878928 9.60643 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 8.791883 8.987806 444.2199 < 2.22e-16 ***
#> s(gdp_per_capita) 8.839470 8.991264 932.8363 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.00813 Deviance explained = 5.93%
#> -REML = -84054 Scale est. = 1 n = 29045
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 8.132137454e-3 very weak (negligible) cohen1988
#> 2 SE 1.004034160e-3 <NA> <NA>
#> 3 Lower CI 6.164266661e-3 very weak (negligible) cohen1988
#> 4 Upper CI 1.010000825e-2 very weak (negligible) cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.863135285e+1
#> 2 logLik 8.414638145e+4
#> 3 AIC -1.682328048e+5
#> 4 BIC -1.679846799e+5
#> 5 deviance 3.189865427e+4
#> 6 df.residual 2.901636865e+4
#> 7 nobs 2.9045000 e+4
#> 8 adj.r.squared 8.132137454e-3
#> 9 npar 2.9 e+1
#>
#> ── Model C ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(93.143)
#> Link function: logit
#>
#> Formula:
#> mpepr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.42693287 0.01923580 -178.15395 < 2.22e-16 ***
#> year2009 0.14213560 0.01937650 7.33546 0.00000000000022095 ***
#> year2011 0.30760210 0.02081891 14.77513 < 2.22e-16 ***
#> year2012 0.03445109 0.02826172 1.21900 0.222844
#> year2013 0.10705705 0.02160162 4.95597 0.00000071969368777 ***
#> year2014 0.11955596 0.02112385 5.65976 0.00000001515823982 ***
#> year2015 0.04888934 0.02950527 1.65697 0.097526 .
#> year2016 0.05441194 0.03247716 1.67539 0.093858 .
#> year2017 0.06812168 0.02766481 2.46239 0.013801 *
#> year2018 0.05337358 0.02853227 1.87064 0.061395 .
#> year2019 0.01036631 0.02792473 0.37122 0.710471
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 6.860406 8.000711 319.3766 < 2.22e-16 ***
#> s(gdp_per_capita) 8.480225 8.919608 254.3667 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0335 Deviance explained = 4.07%
#> -REML = -49541 Scale est. = 1 n = 18633
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 3.354566936e-2 weak cohen1988
#> 2 SE 2.482603924e-3 <NA> <NA>
#> 3 Lower CI 2.867985508e-2 weak cohen1988
#> 4 Upper CI 3.841148364e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.634063135e+1
#> 2 logLik 4.961835964e+4
#> 3 AIC -9.918011725e+4
#> 4 BIC -9.895844413e+4
#> 5 deviance 1.849066434e+4
#> 6 df.residual 1.860665937e+4
#> 7 nobs 1.863300000e+4
#> 8 adj.r.squared 3.354566936e-2
#> 9 npar 2.9 e+1
#>
#> ── Model D ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(118.894)
#> Link function: logit
#>
#> Formula:
#> mpepr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.35738023 0.03476473 -96.57432 < 2e-16 ***
#> year2009 0.06410668 0.04460669 1.43715 0.150674
#> year2011 -0.04569232 0.04535726 -1.00739 0.313749
#> year2012 0.06417669 0.04617055 1.38999 0.164531
#> year2013 0.11348836 0.04451839 2.54925 0.010796 *
#> year2014 0.05762120 0.04571465 1.26045 0.207506
#> year2015 0.06958817 0.05718823 1.21683 0.223670
#> year2016 0.09018290 0.05014183 1.79856 0.072089 .
#> year2017 0.03312795 0.05032558 0.65827 0.510363
#> year2018 -0.03287671 0.04779212 -0.68791 0.491509
#> year2019 -0.03640544 0.04834060 -0.75310 0.451388
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 1.012723 1.025344 0.24008 0.6415545
#> s(gdp_per_capita) 2.940968 3.600515 13.47362 0.0067368 **
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.00808 Deviance explained = 2.01%
#> -REML = -6944 Scale est. = 1 n = 2538
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 8.080351296e-3 very weak (negligible) cohen1988
#> 2 SE 3.381575670e-3 <NA> <NA>
#> 3 Lower CI 1.452584770e-3 very weak (negligible) cohen1988
#> 4 Upper CI 1.470811782e-2 very weak (negligible) cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.495369067e+1
#> 2 logLik 6.982124166e+3
#> 3 AIC -1.393099661e+4
#> 4 BIC -1.383391603e+4
#> 5 deviance 2.488864184e+3
#> 6 df.residual 2.523046309e+3
#> 7 nobs 2.5380 e+3
#> 8 adj.r.squared 8.080351296e-3
#> 9 npar 2.9 e+1Code
mpepr_gam_3_by_misfs |>
summarise_coefs_misfs() |>
md_named_tibble()mpepr_gam_3_by_misfs model.
| A | B | C | D | |
|---|---|---|---|---|
| [Mean] | 0.0036175516 | -0.1026612032 | -0.1293310588 | -0.1108615359 |
| (Intercept) | -3.7055485582 | -4.0378040746 | -3.4269328721 | -3.3573802312 |
| year2009 | -0.0631869374 | 0.1645990559 | 0.1421356011 | 0.0641066751 |
| year2011 | 0.2786461430 | 0.2243943407 | 0.3076020966 | -0.0456923222 |
| year2012 | 0.1963491177 | 0.0746828214 | 0.0344510907 | 0.0641766860 |
| year2013 | 0.3869702640 | 0.3033390653 | 0.1070570500 | 0.1134883565 |
| year2014 | 0.2486958434 | 0.2040997559 | 0.1195559615 | 0.0576211968 |
| year2015 | 0.3719165623 | 0.3645063338 | 0.0488893438 | 0.0695881742 |
| year2016 | 0.3843754730 | 0.4366821085 | 0.0544119352 | 0.0901828956 |
| year2017 | 0.4877324905 | 0.5648437238 | 0.0681216823 | 0.0331279533 |
| year2018 | 0.4819987154 | 0.3520342636 | 0.0533735825 | -0.0328767146 |
| year2019 | 0.2431715455 | 0.2765623291 | 0.0103663149 | -0.0364054369 |
| mean(s(spei_12m)) | 0.0129178557 | -0.0604114187 | 0.0433028759 | 0.0008239560 |
| mean(s(gdp_per_capita)) | 0.0752808484 | -0.1512679831 | -0.1843731526 | -0.0269263754 |
Source: Created by the authors.
Code
dplyr::mutate(data, year = factor(year, ordered = FALSE)) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam_misfs(
gam_models = mpepr_gam_3_by_misfs,
type = 3,
x_label = "Standardised Precipitation Evapotranspiration Index (12 months)",
y_label = "Predicted probability of MPEPR"
)mpepr_gam_3_by_misfs model. All other variables are held constant at their mean values except SPEI. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
dplyr::mutate(data, year = factor(year, ordered = FALSE)) |>
summarise_gam_misfs(maper_mpepr_gam_3_by_misfs)
#>
#> ── Model A ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(24.462)
#> Link function: logit
#>
#> Formula:
#> maper_mpepr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.90691532 0.03519452 -82.59567 < 2.22e-16 ***
#> year2009 -0.04913146 0.05006361 -0.98138 0.32640504
#> year2011 0.20360443 0.04214866 4.83063 0.000001361041698 ***
#> year2012 0.13913958 0.04569320 3.04508 0.00232616 **
#> year2013 0.28798038 0.04325057 6.65842 0.000000000027679 ***
#> year2014 0.20429069 0.04650571 4.39281 0.000011189543781 ***
#> year2015 0.16958041 0.05079507 3.33852 0.00084226 ***
#> year2016 0.23961953 0.05048128 4.74670 0.000002067613268 ***
#> year2017 0.27787958 0.04881537 5.69246 0.000000012522133 ***
#> year2018 0.21448746 0.04599567 4.66321 0.000003113148839 ***
#> year2019 0.02298157 0.05346854 0.42981 0.66733038
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 5.144458 6.380688 42.06683 0.0000021952 ***
#> s(gdp_per_capita) 8.054174 8.752707 120.17626 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.000893 Deviance explained = 3.91%
#> -REML = -13537 Scale est. = 1 n = 7271
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 8.926017278e-4 very weak (negligible) cohen1988
#> 2 SE 6.697671402e-4 <NA> <NA>
#> 3 Lower CI -4.201177451e-4 no effect cohen1988
#> 4 Upper CI 2.205321201e-3 very weak (negligible) cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.419863217e+1
#> 2 logLik 1.359742659e+4
#> 3 AIC -2.714159000e+4
#> 4 BIC -2.695805445e+4
#> 5 deviance 7.323591552e+3
#> 6 df.residual 7.246801368e+3
#> 7 nobs 7.271000000e+3
#> 8 adj.r.squared 8.926017278e-4
#> 9 npar 2.9 e+1
#>
#> ── Model B ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(19.87)
#> Link function: logit
#>
#> Formula:
#> maper_mpepr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.41020431 0.01878661 -181.52309 < 2.22e-16 ***
#> year2009 0.18439888 0.02473011 7.45645 0.000000000000088883 ***
#> year2011 0.18767479 0.02447985 7.66650 0.000000000000017675 ***
#> year2012 0.09290789 0.02654026 3.50064 0.00046414 ***
#> year2013 0.29843151 0.02576282 11.58381 < 2.22e-16 ***
#> year2014 0.22545275 0.02701073 8.34678 < 2.22e-16 ***
#> year2015 0.34685692 0.02566817 13.51311 < 2.22e-16 ***
#> year2016 0.42046596 0.02616450 16.07009 < 2.22e-16 ***
#> year2017 0.54048578 0.02625763 20.58395 < 2.22e-16 ***
#> year2018 0.27900942 0.02675817 10.42707 < 2.22e-16 ***
#> year2019 0.21354545 0.02776013 7.69252 0.000000000000014426 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 8.789591 8.987551 386.7282 < 2.22e-16 ***
#> s(gdp_per_capita) 8.864479 8.993765 1217.6427 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0226 Deviance explained = 6.54%
#> -REML = -64649 Scale est. = 1 n = 29045
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 2.264961359e-2 weak cohen1988
#> 2 SE 1.651098574e-3 <NA> <NA>
#> 3 Lower CI 1.941351985e-2 very weak (negligible) cohen1988
#> 4 Upper CI 2.588570733e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.865407015e+1
#> 2 logLik 6.474207706e+4
#> 3 AIC -1.294241915e+5
#> 4 BIC -1.291760481e+5
#> 5 deviance 3.098039438e+4
#> 6 df.residual 2.901634593e+4
#> 7 nobs 2.9045000 e+4
#> 8 adj.r.squared 2.264961359e-2
#> 9 npar 2.9 e+1
#>
#> ── Model C ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(50.006)
#> Link function: logit
#>
#> Formula:
#> maper_mpepr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.65641913 0.01893243 -140.31054 < 2.22e-16 ***
#> year2009 0.11239445 0.01901003 5.91237 0.0000000033721 ***
#> year2011 0.22419405 0.02057565 10.89609 < 2.22e-16 ***
#> year2012 -0.03574261 0.02822716 -1.26625 0.20542396
#> year2013 0.05253343 0.02126647 2.47025 0.01350198 *
#> year2014 0.03859854 0.02077256 1.85815 0.06314758 .
#> year2015 -0.05229211 0.02942562 -1.77709 0.07555266 .
#> year2016 -0.03228406 0.03243408 -0.99537 0.31955418
#> year2017 -0.02170130 0.02746159 -0.79024 0.42938648
#> year2018 -0.10931082 0.02850843 -3.83433 0.00012591 ***
#> year2019 -0.09452523 0.02773579 -3.40806 0.00065426 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 6.788722 7.942588 230.5865 < 2.22e-16 ***
#> s(gdp_per_capita) 8.177982 8.809404 179.1136 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0335 Deviance explained = 3.95%
#> -REML = -37768 Scale est. = 1 n = 18633
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 3.345831209e-2 weak cohen1988
#> 2 SE 2.479593414e-3 <NA> <NA>
#> 3 Lower CI 2.859839830e-2 weak cohen1988
#> 4 Upper CI 3.831822588e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 2.596670416e+1
#> 2 logLik 3.784267591e+4
#> 3 AIC -7.562915906e+4
#> 4 BIC -7.540908882e+4
#> 5 deviance 1.823334114e+4
#> 6 df.residual 1.860703330e+4
#> 7 nobs 1.863300000e+4
#> 8 adj.r.squared 3.345831209e-2
#> 9 npar 2.9 e+1
#>
#> ── Model D ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(63.388)
#> Link function: logit
#>
#> Formula:
#> maper_mpepr ~ s(spei_12m) + s(gdp_per_capita) + year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.6624175512 0.0348536776 -76.38843 < 2.22e-16 ***
#> year2009 0.0429780409 0.0451113651 0.95271 0.34073711
#> year2011 -0.0830209051 0.0458399077 -1.81111 0.07012454 .
#> year2012 -0.0007241768 0.0469651072 -0.01542 0.98769753
#> year2013 0.0512370729 0.0450887015 1.13636 0.25580522
#> year2014 -0.0163484047 0.0463614791 -0.35263 0.72436655
#> year2015 -0.0095160841 0.0583786292 -0.16301 0.87051348
#> year2016 0.0081128758 0.0509589623 0.15920 0.87350807
#> year2017 -0.0382202897 0.0510231690 -0.74908 0.45381071
#> year2018 -0.1622384524 0.0487656431 -3.32690 0.00087818 ***
#> year2019 -0.1575406806 0.0492276200 -3.20025 0.00137309 **
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(spei_12m) 1.025010 1.049637 0.19522 0.7018100
#> s(gdp_per_capita) 2.222026 2.728323 15.35648 0.0014765 **
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0244 Deviance explained = 3.22%
#> -REML = -5426.8 Scale est. = 1 n = 2538
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 2.435717666e-2 weak cohen1988
#> 2 SE 5.774731859e-3 <NA> <NA>
#> 3 Lower CI 1.303891020e-2 very weak (negligible) cohen1988
#> 4 Upper CI 3.567544313e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.424703656e+1
#> 2 logLik 5.463150490e+3
#> 3 AIC -1.089474506e+4
#> 4 BIC -1.080261548e+4
#> 5 deviance 2.479619569e+3
#> 6 df.residual 2.523752963e+3
#> 7 nobs 2.5380 e+3
#> 8 adj.r.squared 2.435717666e-2
#> 9 npar 2.9 e+1Code
maper_mpepr_gam_3_by_misfs |>
summarise_coefs_misfs() |>
md_named_tibble()maper_mpepr_gam_3_by_misfs model.
| A | B | C | D | |
|---|---|---|---|---|
| [Mean] | -0.0446249356 | -0.0849054516 | -0.1109044570 | -0.1157964318 |
| (Intercept) | -2.9069153226 | -3.4102043134 | -2.6564191262 | -2.6624175512 |
| year2009 | -0.0491314569 | 0.1843988842 | 0.1123944472 | 0.0429780409 |
| year2011 | 0.2036044285 | 0.1876747875 | 0.2241940516 | -0.0830209051 |
| year2012 | 0.1391395772 | 0.0929078941 | -0.0357426134 | -0.0007241768 |
| year2013 | 0.2879803824 | 0.2984315123 | 0.0525334338 | 0.0512370729 |
| year2014 | 0.2042906906 | 0.2254527497 | 0.0385985436 | -0.0163484047 |
| year2015 | 0.1695804142 | 0.3468569173 | -0.0522921123 | -0.0095160841 |
| year2016 | 0.2396195334 | 0.4204659607 | -0.0322840576 | 0.0081128758 |
| year2017 | 0.2778795816 | 0.5404857781 | -0.0217013026 | -0.0382202897 |
| year2018 | 0.2144874637 | 0.2790094159 | -0.1093108210 | -0.1622384524 |
| year2019 | 0.0229815671 | 0.2135454550 | -0.0945252269 | -0.1575406806 |
| mean(s(spei_12m)) | 0.0293925407 | -0.0365198205 | 0.0706258190 | 0.0008421603 |
| mean(s(gdp_per_capita)) | -0.0402414287 | -0.1680671949 | -0.1419229823 | -0.0375530457 |
Source: Created by the authors.
Code
dplyr::mutate(data, year = factor(year, ordered = FALSE)) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam_misfs(
gam_models = maper_mpepr_gam_3_by_misfs,
type = 3,
x_label = "Standardised Precipitation Evapotranspiration Index (12 months)",
y_label = "Predicted probability of MAPER & MPEPR"
)maper_mpepr_gam_3_by_misfs model. All other variables are held constant at their mean values except SPEI. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
By s(year) (Continuous year)
Code
mbepr_gam_4_by_misfs <-
dplyr::mutate(data, year = as.integer(as.character(year))) |>
gam_misfs(mbepr ~ s(year))dplyr::mutate(data, year = as.integer(as.character(year))) |>
summarise_gam_misfs(mbepr_gam_4_by_misfs)
#>
#> ── Model A ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(18.488)
#> Link function: logit
#>
#> Formula:
#> mbepr ~ s(year)
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.764025565 0.008889087 -310.9459 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(year) 7.887682 8.682594 164.6248 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = -0.0196 Deviance explained = 2.27%
#> -REML = -14555 Scale est. = 1 n = 7934
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 8.887681869e+0
#> 2 logLik 1.457885247e+4
#> 3 AIC -2.913653050e+4
#> 4 BIC -2.906264320e+4
#> 5 deviance 8.116224104e+3
#> 6 df.residual 7.925112318e+3
#> 7 nobs 7.93400 e+3
#> 8 adj.r.squared -1.962561973e-2
#> 9 npar 1 e+1
#>
#> ── Model B ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(16.503)
#> Link function: logit
#>
#> Formula:
#> mbepr ~ s(year)
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.067860265 0.004875082 -629.2941 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(year) 7.979043 8.72876 232.1217 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = -0.00452 Deviance explained = 0.756%
#> -REML = -68054 Scale est. = 1 n = 31734
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 8.979042735e+0
#> 2 logLik 6.807959833e+4
#> 3 AIC -1.361377391e+5
#> 4 BIC -1.360479915e+5
#> 5 deviance 3.347287221e+4
#> 6 df.residual 3.172502096e+4
#> 7 nobs 3.1734 e+4
#> 8 adj.r.squared -4.518969525e-3
#> 9 npar 1 e+1
#>
#> ── Model C ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(38.438)
#> Link function: logit
#>
#> Formula:
#> mbepr ~ s(year)
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.601271212 0.004079439 -637.6542 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(year) 8.128049 8.798209 356.0552 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0274 Deviance explained = 1.75%
#> -REML = -38672 Scale est. = 1 n = 20324
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 2.742645089e-2 weak cohen1988
#> 2 SE 2.259216614e-3 <NA> <NA>
#> 3 Lower CI 2.299846769e-2 weak cohen1988
#> 4 Upper CI 3.185443408e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 9.128049307e+0
#> 2 logLik 3.869852716e+4
#> 3 AIC -7.737554990e+4
#> 4 BIC -7.729039715e+4
#> 5 deviance 1.976867118e+4
#> 6 df.residual 2.031487195e+4
#> 7 nobs 2.0324 e+4
#> 8 adj.r.squared 2.742645089e-2
#> 9 npar 1 e+1
#>
#> ── Model D ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(34.962)
#> Link function: logit
#>
#> Formula:
#> mbepr ~ s(year)
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.26870964 0.01027894 -220.7143 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(year) 6.830195 7.938482 131.2971 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0447 Deviance explained = 4.75%
#> -REML = -4662.6 Scale est. = 1 n = 2770
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 4.468165164e-2 weak cohen1988
#> 2 SE 7.663975966e-3 <NA> <NA>
#> 3 Lower CI 2.966053477e-2 weak cohen1988
#> 4 Upper CI 5.970276851e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 7.830194824e+0
#> 2 logLik 4.681903728e+3
#> 3 AIC -9.343930493e+3
#> 4 BIC -9.285029059e+3
#> 5 deviance 2.679398229e+3
#> 6 df.residual 2.762169805e+3
#> 7 nobs 2.77 e+3
#> 8 adj.r.squared 4.468165164e-2
#> 9 npar 1 e+1Code
mbepr_gam_4_by_misfs |>
summarise_coefs_misfs() |>
md_named_tibble()mbepr_gam_4_by_misfs model.
| A | B | C | D | |
|---|---|---|---|---|
| [Mean] | -0.2377084428 | -0.2931434504 | -0.2389874165 | -0.2287300141 |
| (Intercept) | -2.7640255650 | -3.0678602646 | -2.6012712124 | -2.2687096436 |
| mean(s(year)) | 0.0429934597 | 0.0151584178 | 0.0234885609 | -0.0020656109 |
Source: Created by the authors.
Code
dplyr::mutate(data, year = as.integer(as.character(year))) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam_misfs(
gam_models = mbepr_gam_4_by_misfs,
type = 4,
x_label = "Years",
y_label = "Predicted probability of MBEPR"
)mbepr_gam_4_by_misfs model. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
Code
beipr_gam_4_by_misfs <-
dplyr::mutate(data, year = as.integer(as.character(year))) |>
gam_misfs(beipr ~ s(year))dplyr::mutate(data, year = as.integer(as.character(year))) |>
summarise_gam_misfs(beipr_gam_4_by_misfs)
#>
#> ── Model A ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(25.114)
#> Link function: logit
#>
#> Formula:
#> beipr ~ s(year)
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.652246484 0.007815092 -339.375 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(year) 6.840362 7.947109 208.1875 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = -0.028 Deviance explained = 2.66%
#> -REML = -14294 Scale est. = 1 n = 7934
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 7.840362260e+0
#> 2 logLik 1.431385290e+4
#> 3 AIC -2.860796999e+4
#> 4 BIC -2.853910272e+4
#> 5 deviance 8.071653579e+3
#> 6 df.residual 7.926159638e+3
#> 7 nobs 7.93400 e+3
#> 8 adj.r.squared -2.802353414e-2
#> 9 npar 1 e+1
#>
#> ── Model B ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(23.649)
#> Link function: logit
#>
#> Formula:
#> beipr ~ s(year)
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.847564146 0.004210194 -676.3499 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(year) 8.108529 8.789822 259.2185 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = -0.0153 Deviance explained = 0.869%
#> -REML = -61296 Scale est. = 1 n = 31734
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 9.108528612e+0
#> 2 logLik 6.132240410e+4
#> 3 AIC -1.226233722e+5
#> 4 BIC -1.225337147e+5
#> 5 deviance 3.310345549e+4
#> 6 df.residual 3.172489147e+4
#> 7 nobs 3.1734 e+4
#> 8 adj.r.squared -1.533028485e-2
#> 9 npar 1 e+1
#>
#> ── Model C ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(72.181)
#> Link function: logit
#>
#> Formula:
#> beipr ~ s(year)
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.502699587 0.002991543 -836.5916 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(year) 7.538153 8.473267 465.9022 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0356 Deviance explained = 2.24%
#> -REML = -42829 Scale est. = 1 n = 20324
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 3.563220368e-2 weak cohen1988
#> 2 SE 2.553375305e-3 <NA> <NA>
#> 3 Lower CI 3.062768004e-2 weak cohen1988
#> 4 Upper CI 4.063672731e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 8.538153256e+0
#> 2 logLik 4.285311826e+4
#> 3 AIC -8.568632581e+4
#> 4 BIC -8.560748386e+4
#> 5 deviance 2.003209684e+4
#> 6 df.residual 2.031546185e+4
#> 7 nobs 2.0324 e+4
#> 8 adj.r.squared 3.563220368e-2
#> 9 npar 1 e+1
#>
#> ── Model D ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(52.175)
#> Link function: logit
#>
#> Formula:
#> beipr ~ s(year)
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -1.926318771 0.007635733 -252.2769 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(year) 4.985377 6.078625 72.70812 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0342 Deviance explained = 2.7%
#> -REML = -4700.7 Scale est. = 1 n = 2770
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 3.424800961e-2 weak cohen1988
#> 2 SE 6.783044810e-3 <NA> <NA>
#> 3 Lower CI 2.095348608e-2 weak cohen1988
#> 4 Upper CI 4.754253314e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 5.985376796e+0
#> 2 logLik 4.715764580e+3
#> 3 AIC -9.415371910e+3
#> 4 BIC -9.367493110e+3
#> 5 deviance 2.719239612e+3
#> 6 df.residual 2.764014623e+3
#> 7 nobs 2.77 e+3
#> 8 adj.r.squared 3.424800961e-2
#> 9 npar 1 e+1Code
beipr_gam_4_by_misfs |>
summarise_coefs_misfs() |>
md_named_tibble()beipr_gam_4_by_misfs model.
| A | B | C | D | |
|---|---|---|---|---|
| [Mean] | -0.2698576417 | -0.2832120355 | -0.2791948984 | -0.2053964306 |
| (Intercept) | -2.6522464837 | -2.8475641461 | -2.5026995872 | -1.9263187709 |
| mean(s(year)) | -0.0051477703 | 0.0017159768 | -0.0321388219 | -0.0141828373 |
Source: Created by the authors.
Code
dplyr::mutate(data, year = as.integer(as.character(year))) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam_misfs(
gam_models = beipr_gam_4_by_misfs,
type = 4,
x_label = "Years",
y_label = "Predicted probability of BEIPR"
)beipr_gam_4_by_misfs model. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
Code
mbepr_beipr_gam_4_by_misfs <-
dplyr::mutate(data, year = as.integer(as.character(year))) |>
gam_misfs(mbepr_beipr ~ s(year))dplyr::mutate(data, year = as.integer(as.character(year))) |>
summarise_gam_misfs(mbepr_beipr_gam_4_by_misfs)
#>
#> ── Model A ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(17.183)
#> Link function: logit
#>
#> Formula:
#> mbepr_beipr ~ s(year)
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -1.92643518 0.00732242 -263.0872 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(year) 7.487202 8.440969 87.60946 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = -0.00999 Deviance explained = 1.24%
#> -REML = -9877.9 Scale est. = 1 n = 7934
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 8.487202293e+0
#> 2 logLik 9.900141715e+3
#> 3 AIC -1.978032556e+4
#> 4 BIC -1.971068344e+4
#> 5 deviance 7.755904132e+3
#> 6 df.residual 7.925512798e+3
#> 7 nobs 7.93400 e+3
#> 8 adj.r.squared -9.992387590e-3
#> 9 npar 1 e+1
#>
#> ── Model B ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(16.446)
#> Link function: logit
#>
#> Formula:
#> mbepr_beipr ~ s(year)
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.201625036 0.004007156 -549.4234 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(year) 8.090503 8.781786 158.3798 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = -0.00203 Deviance explained = 0.545%
#> -REML = -44239 Scale est. = 1 n = 31734
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 9.090502994e+0
#> 2 logLik 4.426560120e+4
#> 3 AIC -8.851017443e+4
#> 4 BIC -8.842222342e+4
#> 5 deviance 3.182801932e+4
#> 6 df.residual 3.172490950e+4
#> 7 nobs 3.1734 e+4
#> 8 adj.r.squared -2.025155691e-3
#> 9 npar 1 e+1
#>
#> ── Model C ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(32.282)
#> Link function: logit
#>
#> Formula:
#> mbepr_beipr ~ s(year)
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -1.77538891 0.00334683 -530.4687 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(year) 7.448459 8.413178 720.6691 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0428 Deviance explained = 3.42%
#> -REML = -28936 Scale est. = 1 n = 20324
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 4.276223341e-2 weak cohen1988
#> 2 SE 2.776518861e-3 <NA> <NA>
#> 3 Lower CI 3.732035644e-2 weak cohen1988
#> 4 Upper CI 4.820411038e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 8.448458557e+0
#> 2 logLik 2.895922531e+4
#> 3 AIC -5.789834457e+4
#> 4 BIC -5.781872905e+4
#> 5 deviance 1.982184104e+4
#> 6 df.residual 2.031555154e+4
#> 7 nobs 2.0324 e+4
#> 8 adj.r.squared 4.276223341e-2
#> 9 npar 1 e+1
#>
#> ── Model D ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(24.301)
#> Link function: logit
#>
#> Formula:
#> mbepr_beipr ~ s(year)
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -1.259433674 0.008937905 -140.9093 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(year) 5.628751 6.781089 149.8307 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0565 Deviance explained = 5.35%
#> -REML = -3049.2 Scale est. = 1 n = 2770
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 5.650386597e-2 weak cohen1988
#> 2 SE 8.511784358e-3 <NA> <NA>
#> 3 Lower CI 3.982107519e-2 weak cohen1988
#> 4 Upper CI 7.318665676e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 6.628751260e+0
#> 2 logLik 3.065513233e+3
#> 3 AIC -6.113464288e+3
#> 4 BIC -6.061422264e+3
#> 5 deviance 2.689338651e+3
#> 6 df.residual 2.763371249e+3
#> 7 nobs 2.77 e+3
#> 8 adj.r.squared 5.650386597e-2
#> 9 npar 1 e+1Code
mbepr_beipr_gam_4_by_misfs |>
summarise_coefs_misfs() |>
md_named_tibble()mbepr_beipr_gam_4_by_misfs model.
| A | B | C | D | |
|---|---|---|---|---|
| [Mean] | -0.1746701213 | -0.2132274763 | -0.1905945030 | -0.1399896646 |
| (Intercept) | -1.9264351823 | -2.2016250356 | -1.7753889106 | -1.2594336745 |
| mean(s(year)) | 0.0199704410 | 0.0077055858 | -0.0145062355 | -0.0156069969 |
Source: Created by the authors.
Code
dplyr::mutate(data, year = as.integer(as.character(year))) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam_misfs(
gam_models = mbepr_beipr_gam_4_by_misfs,
type = 4,
x_label = "Years",
y_label = "Predicted probability of MBEPR & BEIPR"
)
#> Warning: Removed 500 rows containing missing values or values outside the scale range
#> (`geom_line()`).
#> Warning in max(ids, na.rm = TRUE): no non-missing arguments to max;
#> returning -Infmbepr_beipr_gam_4_by_misfs model. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
Code
maper_gam_4_by_misfs <-
dplyr::mutate(data, year = as.integer(as.character(year))) |>
gam_misfs(maper ~ s(year))dplyr::mutate(data, year = as.integer(as.character(year))) |>
summarise_gam_misfs(maper_gam_4_by_misfs)
#>
#> ── Model A ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(23.728)
#> Link function: logit
#>
#> Formula:
#> maper ~ s(year)
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.528361904 0.009798933 -360.0761 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(year) 6.71971 7.844291 67.31148 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = -0.0075 Deviance explained = 0.876%
#> -REML = -20724 Scale est. = 1 n = 7934
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 7.719710001e+0
#> 2 logLik 2.074295858e+4
#> 3 AIC -4.146622857e+4
#> 4 BIC -4.139752613e+4
#> 5 deviance 8.431395374e+3
#> 6 df.residual 7.926280290e+3
#> 7 nobs 7.93400 e+3
#> 8 adj.r.squared -7.504047063e-3
#> 9 npar 1 e+1
#>
#> ── Model B ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(22.999)
#> Link function: logit
#>
#> Formula:
#> maper ~ s(year)
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.947469608 0.005229374 -754.8647 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(year) 8.024324 8.750592 174.1822 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = -0.00274 Deviance explained = 0.525%
#> -REML = -1.0447e+05 Scale est. = 1 n = 31734
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 9.024323628e+0
#> 2 logLik 1.044963446e+5
#> 3 AIC -2.089711881e+5
#> 4 BIC -2.088812579e+5
#> 5 deviance 3.427273799e+4
#> 6 df.residual 3.172497568e+4
#> 7 nobs 3.1734 e+4
#> 8 adj.r.squared -2.739061946e-3
#> 9 npar 1 e+1
#>
#> ── Model C ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(51.579)
#> Link function: logit
#>
#> Formula:
#> maper ~ s(year)
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.400230669 0.004764297 -713.6899 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(year) 8.434371 8.911811 207.0213 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0114 Deviance explained = 1.09%
#> -REML = -50956 Scale est. = 1 n = 20324
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 1.137519129e-2 very weak (negligible) cohen1988
#> 2 SE 1.478977177e-3 <NA> <NA>
#> 3 Lower CI 8.476449290e-3 very weak (negligible) cohen1988
#> 4 Upper CI 1.427393329e-2 very weak (negligible) cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 9.434370799e+0
#> 2 logLik 5.098456076e+4
#> 3 AIC -1.019472979e+5
#> 4 BIC -1.018608812e+5
#> 5 deviance 2.004291470e+4
#> 6 df.residual 2.031456563e+4
#> 7 nobs 2.0324 e+4
#> 8 adj.r.squared 1.137519129e-2
#> 9 npar 1 e+1
#>
#> ── Model D ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(84.051)
#> Link function: logit
#>
#> Formula:
#> maper ~ s(year)
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.51494952 0.01117707 -314.4786 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(year) 3.812015 4.7125 46.05516 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0231 Deviance explained = 1.89%
#> -REML = -7553.9 Scale est. = 1 n = 2770
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 2.307311496e-2 weak cohen1988
#> 2 SE 5.631921366e-3 <NA> <NA>
#> 3 Lower CI 1.203475192e-2 very weak (negligible) cohen1988
#> 4 Upper CI 3.411147800e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 4.812015363e+0
#> 2 logLik 7.565617215e+3
#> 3 AIC -1.511780943e+4
#> 4 BIC -1.507802711e+4
#> 5 deviance 2.709463766e+3
#> 6 df.residual 2.765187985e+3
#> 7 nobs 2.77 e+3
#> 8 adj.r.squared 2.307311496e-2
#> 9 npar 1 e+1Code
maper_gam_4_by_misfs |>
summarise_coefs_misfs() |>
md_named_tibble()maper_gam_4_by_misfs model.
| A | B | C | D | |
|---|---|---|---|---|
| [Mean] | -0.3396719578 | -0.3745725713 | -0.2704610202 | -0.3506199485 |
| (Intercept) | -3.5283619041 | -3.9474696080 | -3.4002306687 | -3.5149495213 |
| mean(s(year)) | 0.0146269251 | 0.0224159884 | 0.0772911630 | 0.0009722263 |
Source: Created by the authors.
Code
dplyr::mutate(data, year = as.integer(as.character(year))) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam_misfs(
gam_models = maper_gam_4_by_misfs,
type = 4,
x_label = "Years",
y_label = "Predicted probability of MAPER"
)maper_gam_4_by_misfs model. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
Code
mpepr_gam_4_by_misfs <-
dplyr::mutate(data, year = as.integer(as.character(year))) |>
gam_misfs(mpepr ~ s(year))dplyr::mutate(data, year = as.integer(as.character(year))) |>
summarise_gam_misfs(mpepr_gam_4_by_misfs)
#>
#> ── Model A ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(31.016)
#> Link function: logit
#>
#> Formula:
#> mpepr ~ s(year)
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.415780792 0.008982098 -380.2876 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(year) 5.876832 7.041259 144.7022 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = -0.0331 Deviance explained = 1.82%
#> -REML = -19446 Scale est. = 1 n = 7934
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 6.876831913e+0
#> 2 logLik 1.946273819e+4
#> 3 AIC -3.890744891e+4
#> 4 BIC -3.884454287e+4
#> 5 deviance 8.410916411e+3
#> 6 df.residual 7.927123168e+3
#> 7 nobs 7.93400 e+3
#> 8 adj.r.squared -3.306336093e-2
#> 9 npar 1 e+1
#>
#> ── Model B ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(25.89)
#> Link function: logit
#>
#> Formula:
#> mpepr ~ s(year)
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.737458578 0.004989861 -749.0105 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(year) 8.129835 8.799041 388.3712 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = -0.00817 Deviance explained = 1.12%
#> -REML = -90893 Scale est. = 1 n = 31734
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 9.129834919e+0
#> 2 logLik 9.091881222e+4
#> 3 AIC -1.818160264e+5
#> 4 BIC -1.817256908e+5
#> 5 deviance 3.487152626e+4
#> 6 df.residual 3.172487017e+4
#> 7 nobs 3.1734 e+4
#> 8 adj.r.squared -8.168167937e-3
#> 9 npar 1 e+1
#>
#> ── Model C ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(87.956)
#> Link function: logit
#>
#> Formula:
#> mpepr ~ s(year)
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.328906026 0.003775039 -881.8204 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(year) 5.87848 7.04167 125.3592 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.00837 Deviance explained = 0.658%
#> -REML = -53490 Scale est. = 1 n = 20324
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 8.368181294e-3 very weak (negligible) cohen1988
#> 2 SE 1.272379336e-3 <NA> <NA>
#> 3 Lower CI 5.874363621e-3 very weak (negligible) cohen1988
#> 4 Upper CI 1.086199897e-2 very weak (negligible) cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 6.878479732e+0
#> 2 logLik 5.350847177e+4
#> 3 AIC -1.069996254e+5
#> 4 BIC -1.069310493e+5
#> 5 deviance 2.018204211e+4
#> 6 df.residual 2.031712152e+4
#> 7 nobs 2.0324 e+4
#> 8 adj.r.squared 8.368181294e-3
#> 9 npar 1 e+1
#>
#> ── Model D ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(117.221)
#> Link function: logit
#>
#> Formula:
#> mpepr ~ s(year)
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.316663217 0.008995402 -368.7065 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(year) 2.804893 3.488528 18.45051 0.00068947 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.00962 Deviance explained = 0.78%
#> -REML = -7579.6 Scale est. = 1 n = 2770
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 9.620417112e-3 very weak (negligible) cohen1988
#> 2 SE 3.686718987e-3 <NA> <NA>
#> 3 Lower CI 2.394580677e-3 very weak (negligible) cohen1988
#> 4 Upper CI 1.684625355e-2 very weak (negligible) cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 3.804893450e+0
#> 2 logLik 7.589756430e+3
#> 3 AIC -1.516853580e+4
#> 4 BIC -1.513600748e+4
#> 5 deviance 2.724408547e+3
#> 6 df.residual 2.766195107e+3
#> 7 nobs 2.77 e+3
#> 8 adj.r.squared 9.620417112e-3
#> 9 npar 1 e+1Code
mpepr_gam_4_by_misfs |>
summarise_coefs_misfs() |>
md_named_tibble()mpepr_gam_4_by_misfs model.
| A | B | C | D | |
|---|---|---|---|---|
| [Mean] | -0.3654426529 | -0.3880494502 | -0.3385856281 | -0.3298481889 |
| (Intercept) | -3.4157807917 | -3.7374585778 | -3.3289060256 | -3.3166632172 |
| mean(s(year)) | -0.0265161931 | -0.0158928805 | -0.0063278061 | 0.0020201475 |
Source: Created by the authors.
Code
dplyr::mutate(data, year = as.integer(as.character(year))) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam_misfs(
gam_models = mpepr_gam_4_by_misfs,
type = 4,
x_label = "Years",
y_label = "Predicted probability of MPEPR"
)mpepr_gam_4_by_misfs model. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
Code
maper_mpepr_gam_4_by_misfs <-
dplyr::mutate(data, year = as.integer(as.character(year))) |>
gam_misfs(maper_mpepr ~ s(year))dplyr::mutate(data, year = as.integer(as.character(year))) |>
summarise_gam_misfs(maper_mpepr_gam_4_by_misfs)
#>
#> ── Model A ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(23.501)
#> Link function: logit
#>
#> Formula:
#> maper_mpepr ~ s(year)
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.738267001 0.008190896 -334.3062 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(year) 5.355141 6.489999 77.43736 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = -0.00878 Deviance explained = 1.06%
#> -REML = -14650 Scale est. = 1 n = 7934
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 6.355141079e+0
#> 2 logLik 1.466593064e+4
#> 3 AIC -2.931488128e+4
#> 4 BIC -2.925563031e+4
#> 5 deviance 8.013236128e+3
#> 6 df.residual 7.927644859e+3
#> 7 nobs 7.93400 e+3
#> 8 adj.r.squared -8.779179357e-3
#> 9 npar 1 e+1
#>
#> ── Model B ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(18.304)
#> Link function: logit
#>
#> Formula:
#> maper_mpepr ~ s(year)
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.123772043 0.004812238 -649.1308 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(year) 8.468487 8.921806 306.6465 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = -0.00354 Deviance explained = 0.906%
#> -REML = -69448 Scale est. = 1 n = 31734
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 9.468486987e+0
#> 2 logLik 6.947625515e+4
#> 3 AIC -1.389306667e+5
#> 4 BIC -1.388393042e+5
#> 5 deviance 3.380077243e+4
#> 6 df.residual 3.172453151e+4
#> 7 nobs 3.1734 e+4
#> 8 adj.r.squared -3.543446137e-3
#> 9 npar 1 e+1
#>
#> ── Model C ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(47.018)
#> Link function: logit
#>
#> Formula:
#> maper_mpepr ~ s(year)
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.63405992 0.00379428 -694.2186 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(year) 6.82548 7.933766 282.1114 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0205 Deviance explained = 1.46%
#> -REML = -40579 Scale est. = 1 n = 20324
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 2.054835475e-2 weak cohen1988
#> 2 SE 1.969346524e-3 <NA> <NA>
#> 3 Lower CI 1.668850649e-2 very weak (negligible) cohen1988
#> 4 Upper CI 2.440820301e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 7.825479515e+0
#> 2 logLik 4.060058114e+4
#> 3 AIC -8.118129475e+4
#> 4 BIC -8.110262372e+4
#> 5 deviance 1.989189348e+4
#> 6 df.residual 2.031617452e+4
#> 7 nobs 2.0324 e+4
#> 8 adj.r.squared 2.054835475e-2
#> 9 npar 1 e+1
#>
#> ── Model D ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(60.892)
#> Link function: logit
#>
#> Formula:
#> maper_mpepr ~ s(year)
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.684274755 0.009366149 -286.5932 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(year) 3.118664 3.873412 48.69109 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> R-sq.(adj) = 0.0245 Deviance explained = 1.94%
#> -REML = -5884.9 Scale est. = 1 n = 2770
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 2.445679373e-2 weak cohen1988
#> 2 SE 5.790121474e-3 <NA> <NA>
#> 3 Lower CI 1.310836418e-2 very weak (negligible) cohen1988
#> 4 Upper CI 3.580522329e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 4.118664335e+0
#> 2 logLik 5.895557018e+3
#> 3 AIC -1.177936721e+4
#> 4 BIC -1.174455783e+4
#> 5 deviance 2.711925400e+3
#> 6 df.residual 2.765881336e+3
#> 7 nobs 2.77 e+3
#> 8 adj.r.squared 2.445679373e-2
#> 9 npar 1 e+1Code
maper_mpepr_gam_4_by_misfs |>
summarise_coefs_misfs() |>
md_named_tibble()maper_mpepr_gam_4_by_misfs model.
| A | B | C | D | |
|---|---|---|---|---|
| [Mean] | -0.2785507367 | -0.3102520032 | -0.2486774600 | -0.2695130778 |
| (Intercept) | -2.7382670006 | -3.1237720431 | -2.6340599206 | -2.6842747551 |
| mean(s(year)) | -0.0052489296 | 0.0023613345 | 0.0163650357 | -0.0012062247 |
Source: Created by the authors.
Code
dplyr::mutate(data, year = as.integer(as.character(year))) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam_misfs(
gam_models = maper_mpepr_gam_4_by_misfs,
type = 4,
x_label = "Years",
y_label = "Predicted probability of MAPER & MPEPR"
)maper_mpepr_gam_4_by_misfs model. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
By year (Ordered)
In this model, the year variable is treated as a ordered categorical variable.
.L, .Q, and .C are, respectively, the coefficients for the ordered factor coded with linear, quadratic, and cubic contrasts.
Code
mbepr_gam_5_by_misfs <-
data |>
gam_misfs(mbepr ~ year)data |>
summarise_gam_misfs(mbepr_gam_5_by_misfs)
#>
#> ── Model A ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(18.537)
#> Link function: logit
#>
#> Formula:
#> mbepr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.76707348 0.00889582 -311.05322 < 2.22e-16 ***
#> year.L 0.28304655 0.03121408 9.06791 < 2.22e-16 ***
#> year.Q -0.11246535 0.03138404 -3.58352 0.00033899 ***
#> year.C 0.04686843 0.03131901 1.49648 0.13452735
#> year^4 -0.13966641 0.03090395 -4.51937 0.00000620235717360 ***
#> year^5 0.22113383 0.03081657 7.17581 0.00000000000071881 ***
#> year^6 -0.10484629 0.03047211 -3.44073 0.00058015 ***
#> year^7 -0.05267022 0.03059111 -1.72175 0.08511499 .
#> year^8 0.05572956 0.03054007 1.82480 0.06803102 .
#> year^9 -0.05530103 0.03045136 -1.81604 0.06936350 .
#> year^10 -0.11170879 0.03077141 -3.63028 0.00028312 ***
#> year^11 -0.05494166 0.03049266 -1.80180 0.07157702 .
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = -0.0203 Deviance explained = 2.47%
#> -REML = -14555 Scale est. = 1 n = 7934
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 1.458696428e+4
#> 3 AIC -2.914792856e+4
#> 4 BIC -2.905720269e+4
#> 5 deviance 8.119205011e+3
#> 6 df.residual 7.922 e+3
#> 7 nobs 7.93400 e+3
#> 8 adj.r.squared -2.027317837e-2
#> 9 npar 1.2 e+1
#>
#> ── Model B ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(16.507)
#> Link function: logit
#>
#> Formula:
#> mbepr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.068257280 0.004876622 -629.17683 < 2.22e-16 ***
#> year.L 0.117916909 0.016977423 6.94551 0.0000000000037709 ***
#> year.Q -0.174826699 0.017095705 -10.22635 < 2.22e-16 ***
#> year.C -0.003230379 0.016997114 -0.19005 0.8492664
#> year^4 -0.092998354 0.016928528 -5.49359 0.0000000393849543 ***
#> year^5 0.113903431 0.016871638 6.75118 0.0000000000146649 ***
#> year^6 -0.053888234 0.016821582 -3.20352 0.0013576 **
#> year^7 -0.005140243 0.016788872 -0.30617 0.7594755
#> year^8 0.051135768 0.016775518 3.04824 0.0023019 **
#> year^9 -0.024217553 0.016789792 -1.44240 0.1491903
#> year^10 -0.030014231 0.016842341 -1.78207 0.0747378 .
#> year^11 -0.007893006 0.016932609 -0.46614 0.6411136
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = -0.00456 Deviance explained = 0.764%
#> -REML = -68042 Scale est. = 1 n = 31734
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 6.808076769e+4
#> 3 AIC -1.361355354e+5
#> 4 BIC -1.360267885e+5
#> 5 deviance 3.347652301e+4
#> 6 df.residual 3.1722 e+4
#> 7 nobs 3.1734 e+4
#> 8 adj.r.squared -4.559784873e-3
#> 9 npar 1.2 e+1
#>
#> ── Model C ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(38.489)
#> Link function: logit
#>
#> Formula:
#> mbepr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.601124170 0.004077341 -637.94616 < 2.22e-16 ***
#> year.L -0.221239238 0.014086278 -15.70601 < 2.22e-16 ***
#> year.Q 0.078115440 0.014179186 5.50916 0.000000036054493 ***
#> year.C 0.005758650 0.014116639 0.40793 0.68332249
#> year^4 -0.058430541 0.014093349 -4.14597 0.000033838461198 ***
#> year^5 0.068477692 0.014150746 4.83916 0.000001303904250 ***
#> year^6 0.002665934 0.014041834 0.18986 0.84942154
#> year^7 -0.007964157 0.014126746 -0.56376 0.57291445
#> year^8 0.046695378 0.014092086 3.31359 0.00092107 ***
#> year^9 -0.002246625 0.014028708 -0.16014 0.87276696
#> year^10 -0.094569778 0.014214460 -6.65307 0.000000000028704 ***
#> year^11 -0.023171492 0.014235985 -1.62767 0.10359478
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = 0.0285 Deviance explained = 1.87%
#> -REML = -38670 Scale est. = 1 n = 20324
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 2.851689999e-2 weak cohen1988
#> 2 SE 2.301108092e-3 <NA> <NA>
#> 3 Lower CI 2.400681100e-2 weak cohen1988
#> 4 Upper CI 3.302698897e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 3.871102690e+4
#> 3 AIC -7.739605379e+4
#> 4 BIC -7.729309954e+4
#> 5 deviance 1.976947966e+4
#> 6 df.residual 2.03120000 e+4
#> 7 nobs 2.0324 e+4
#> 8 adj.r.squared 2.851689999e-2
#> 9 npar 1.2 e+1
#>
#> ── Model D ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(35.093)
#> Link function: logit
#>
#> Formula:
#> mbepr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.268126583 0.010262308 -221.01525 < 2.22e-16 ***
#> year.L -0.349342664 0.035482444 -9.84551 < 2.22e-16 ***
#> year.Q 0.118855625 0.035612748 3.33745 0.00084552 ***
#> year.C -0.007878134 0.035733439 -0.22047 0.82550551
#> year^4 -0.019372846 0.035323568 -0.54844 0.58339004
#> year^5 0.087681548 0.035681486 2.45734 0.01399701 *
#> year^6 -0.083700324 0.035219866 -2.37651 0.01747734 *
#> year^7 -0.025897709 0.035565035 -0.72818 0.46650407
#> year^8 0.100549311 0.035482342 2.83378 0.00460003 **
#> year^9 0.039742476 0.035343749 1.12446 0.26081979
#> year^10 -0.141721586 0.036103188 -3.92546 0.000086564 ***
#> year^11 -0.005692148 0.035490482 -0.16039 0.87257765
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = 0.0455 Deviance explained = 5.16%
#> -REML = -4657.5 Scale est. = 1 n = 2770
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 4.545270470e-2 weak cohen1988
#> 2 SE 7.723581311e-3 <NA> <NA>
#> 3 Lower CI 3.031476350e-2 weak cohen1988
#> 4 Upper CI 6.059064590e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 4.687741024e+3
#> 3 AIC -9.349482048e+3
#> 4 BIC -9.272436214e+3
#> 5 deviance 2.677966059e+3
#> 6 df.residual 2.758 e+3
#> 7 nobs 2.77 e+3
#> 8 adj.r.squared 4.545270470e-2
#> 9 npar 1.2 e+1Code
mbepr_gam_5_by_misfs |>
summarise_coefs_misfs() |>
md_named_tibble()mbepr_gam_5_by_misfs model.
| A | B | C | D | |
|---|---|---|---|---|
| [Mean] | -0.2326579044 | -0.2647924893 | -0.2339194089 | -0.2129085861 |
| (Intercept) | -2.7670734755 | -3.0682572798 | -2.6011241702 | -2.2681265826 |
| year.L | 0.2830465530 | 0.1179169093 | -0.2212392381 | -0.3493426642 |
| year.Q | -0.1124653465 | -0.1748266989 | 0.0781154405 | 0.1188556253 |
| year.C | 0.0468684280 | -0.0032303794 | 0.0057586501 | -0.0078781339 |
| year^4 | -0.1396664095 | -0.0929983540 | -0.0584305407 | -0.0193728460 |
| year^5 | 0.2211338304 | 0.1139034310 | 0.0684776920 | 0.0876815480 |
| year^6 | -0.1048462941 | -0.0538882343 | 0.0026659342 | -0.0837003236 |
| year^7 | -0.0526702159 | -0.0051402433 | -0.0079641573 | -0.0258977089 |
| year^8 | 0.0557295546 | 0.0511357681 | 0.0466953784 | 0.1005493105 |
| year^9 | -0.0553010304 | -0.0242175533 | -0.0022466255 | 0.0397424761 |
| year^10 | -0.1117087910 | -0.0300142310 | -0.0945697779 | -0.1417215861 |
| year^11 | -0.0549416555 | -0.0078930063 | -0.0231714925 | -0.0056921479 |
Source: Created by the authors.
Code
data |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam_misfs(
gam_models = mbepr_gam_5_by_misfs,
type = 5,
x_label = "Years",
y_label = "Predicted probability of MBEPR"
)mbepr_gam_5_by_misfs model. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
Code
beipr_gam_5_by_misfs <-
data |>
gam_misfs(beipr ~ year)data |>
summarise_gam_misfs(beipr_gam_5_by_misfs)
#>
#> ── Model A ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(25.127)
#> Link function: logit
#>
#> Formula:
#> beipr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.653683063 0.007822268 -339.24725 < 2.22e-16 ***
#> year.L 0.363126602 0.027254975 13.32331 < 2.22e-16 ***
#> year.Q 0.006592482 0.027315449 0.24135 0.8092867
#> year.C -0.067126106 0.027355416 -2.45385 0.0141336 *
#> year^4 -0.026716047 0.027091455 -0.98614 0.3240630
#> year^5 0.072639093 0.027086258 2.68177 0.0073234 **
#> year^6 -0.067121673 0.026968738 -2.48887 0.0128150 *
#> year^7 -0.106999017 0.026960591 -3.96872 0.00007226 ***
#> year^8 0.049467750 0.026962598 1.83468 0.0665531 .
#> year^9 0.016125260 0.027014572 0.59691 0.5505677
#> year^10 -0.019663087 0.027145861 -0.72435 0.4688513
#> year^11 0.027474518 0.026908162 1.02105 0.3072318
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = -0.0299 Deviance explained = 2.71%
#> -REML = -14282 Scale est. = 1 n = 7934
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 1.431571354e+4
#> 3 AIC -2.860542709e+4
#> 4 BIC -2.851470122e+4
#> 5 deviance 8.071957558e+3
#> 6 df.residual 7.922 e+3
#> 7 nobs 7.93400 e+3
#> 8 adj.r.squared -2.986476328e-2
#> 9 npar 1.2 e+1
#>
#> ── Model B ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(23.666)
#> Link function: logit
#>
#> Formula:
#> beipr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.848403801 0.004212082 -676.24608 < 2.22e-16 ***
#> year.L 0.164472875 0.014594109 11.26981 < 2.22e-16 ***
#> year.Q -0.042234319 0.014759944 -2.86141 0.0042176 **
#> year.C -0.026048138 0.014657237 -1.77715 0.0755432 .
#> year^4 -0.102261347 0.014581803 -7.01294 2.3336e-12 ***
#> year^5 0.113377180 0.014552940 7.79067 6.6654e-15 ***
#> year^6 -0.033556378 0.014535455 -2.30859 0.0209665 *
#> year^7 -0.042350207 0.014462416 -2.92829 0.0034083 **
#> year^8 0.061968334 0.014463510 4.28446 1.8318e-05 ***
#> year^9 -0.008431711 0.014541208 -0.57985 0.5620162
#> year^10 0.012862093 0.014613024 0.88018 0.3787618
#> year^11 0.062101003 0.014736983 4.21396 2.5094e-05 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = -0.0159 Deviance explained = 0.926%
#> -REML = -61291 Scale est. = 1 n = 31734
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 6.133176478e+4
#> 3 AIC -1.226375296e+5
#> 4 BIC -1.225287827e+5
#> 5 deviance 3.310622465e+4
#> 6 df.residual 3.1722 e+4
#> 7 nobs 3.1734 e+4
#> 8 adj.r.squared -1.591864228e-2
#> 9 npar 1.2 e+1
#>
#> ── Model C ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(72.251)
#> Link function: logit
#>
#> Formula:
#> beipr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.502196791 0.002989478 -837.00117 < 2.22e-16 ***
#> year.L -0.148795186 0.010256389 -14.50756 < 2.22e-16 ***
#> year.Q 0.140467010 0.010344901 13.57838 < 2.22e-16 ***
#> year.C -0.015295539 0.010349307 -1.47793 0.13942683
#> year^4 -0.045210704 0.010310435 -4.38495 0.0000116015 ***
#> year^5 0.031196138 0.010306005 3.02699 0.00247005 **
#> year^6 -0.048162565 0.010293102 -4.67911 0.0000028812 ***
#> year^7 -0.027614694 0.010329294 -2.67343 0.00750789 **
#> year^8 0.015704477 0.010361007 1.51573 0.12958795
#> year^9 0.024284210 0.010396450 2.33582 0.01950075 *
#> year^10 -0.026072357 0.010468922 -2.49045 0.01275804 *
#> year^11 0.035524684 0.010496031 3.38458 0.00071287 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = 0.036 Deviance explained = 2.34%
#> -REML = -42819 Scale est. = 1 n = 20324
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 3.600156273e-2 weak cohen1988
#> 2 SE 2.565592159e-3 <NA> <NA>
#> 3 Lower CI 3.097309450e-2 weak cohen1988
#> 4 Upper CI 4.103003096e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 4.286366655e+4
#> 3 AIC -8.570133310e+4
#> 4 BIC -8.559837885e+4
#> 5 deviance 2.003054550e+4
#> 6 df.residual 2.03120000 e+4
#> 7 nobs 2.0324 e+4
#> 8 adj.r.squared 3.600156273e-2
#> 9 npar 1.2 e+1
#>
#> ── Model D ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(52.212)
#> Link function: logit
#>
#> Formula:
#> beipr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -1.925855145 0.007633206 -252.29966 < 2.22e-16 ***
#> year.L -0.197665440 0.026515721 -7.45465 0.000000000000090106 ***
#> year.Q 0.061061663 0.026628696 2.29308 0.021844 *
#> year.C 0.056733481 0.026641358 2.12953 0.033211 *
#> year^4 -0.048045087 0.026391217 -1.82050 0.068684 .
#> year^5 0.037930444 0.026437739 1.43471 0.151370
#> year^6 -0.065299046 0.026322574 -2.48072 0.013112 *
#> year^7 -0.006545489 0.026302884 -0.24885 0.803476
#> year^8 0.048114722 0.026298952 1.82953 0.067320 .
#> year^9 0.010639848 0.026374879 0.40341 0.686648
#> year^10 -0.022898650 0.026567896 -0.86189 0.388747
#> year^11 0.009279899 0.026379237 0.35179 0.724997
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = 0.0327 Deviance explained = 2.94%
#> -REML = -4685.3 Scale est. = 1 n = 2770
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 3.271189059e-2 weak cohen1988
#> 2 SE 6.639724773e-3 <NA> <NA>
#> 3 Lower CI 1.969826917e-2 very weak (negligible) cohen1988
#> 4 Upper CI 4.572551202e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 4.719121470e+3
#> 3 AIC -9.412242941e+3
#> 4 BIC -9.335197107e+3
#> 5 deviance 2.714505806e+3
#> 6 df.residual 2.758000000e+3
#> 7 nobs 2.77 e+3
#> 8 adj.r.squared 3.271189059e-2
#> 9 npar 1.2 e+1Code
beipr_gam_5_by_misfs |>
summarise_coefs_misfs() |>
md_named_tibble()beipr_gam_5_by_misfs model.
| A | B | C | D | |
|---|---|---|---|---|
| [Mean] | -0.2004902740 | -0.2240420346 | -0.2138476097 | -0.1702124000 |
| (Intercept) | -2.6536830628 | -2.8484038009 | -2.5021967911 | -1.9258551452 |
| year.L | 0.3631266025 | 0.1644728747 | -0.1487951861 | -0.1976654395 |
| year.Q | 0.0065924824 | -0.0422343195 | 0.1404670099 | 0.0610616633 |
| year.C | -0.0671261060 | -0.0260481377 | -0.0152955393 | 0.0567334811 |
| year^4 | -0.0267160475 | -0.1022613469 | -0.0452107036 | -0.0480450874 |
| year^5 | 0.0726390926 | 0.1133771804 | 0.0311961381 | 0.0379304436 |
| year^6 | -0.0671216726 | -0.0335563782 | -0.0481625652 | -0.0652990463 |
| year^7 | -0.1069990172 | -0.0423502066 | -0.0276146937 | -0.0065454890 |
| year^8 | 0.0494677502 | 0.0619683345 | 0.0157044771 | 0.0481147218 |
| year^9 | 0.0161252596 | -0.0084317112 | 0.0242842104 | 0.0106398483 |
| year^10 | -0.0196630871 | 0.0128620929 | -0.0260723572 | -0.0228986497 |
| year^11 | 0.0274745179 | 0.0621010034 | 0.0355246842 | 0.0092798991 |
Source: Created by the authors.
Code
data |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam_misfs(
gam_models = beipr_gam_5_by_misfs,
type = 5,
x_label = "Years",
y_label = "Predicted probability of BEIPR"
)beipr_gam_5_by_misfs model. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
Code
mbepr_beipr_gam_5_by_misfs <-
data |>
gam_misfs(mbepr_beipr ~ year)data |>
summarise_gam_misfs(mbepr_beipr_gam_5_by_misfs)
#>
#> ── Model A ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(17.202)
#> Link function: logit
#>
#> Formula:
#> mbepr_beipr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -1.927800978 0.007327002 -263.10912 < 2.22e-16 ***
#> year.L 0.155049954 0.025596459 6.05748 0.0000000013827 ***
#> year.Q -0.034396274 0.025664489 -1.34023 0.1801711
#> year.C -0.006036878 0.025713990 -0.23477 0.8143871
#> year^4 -0.048352778 0.025401956 -1.90351 0.0569745 .
#> year^5 0.144445424 0.025364494 5.69479 0.0000000123525 ***
#> year^6 -0.104062168 0.025157411 -4.13644 0.0000352732685 ***
#> year^7 -0.040925467 0.025253863 -1.62056 0.1051115
#> year^8 0.048076497 0.025252105 1.90386 0.0569283 .
#> year^9 -0.005973620 0.025227551 -0.23679 0.8128201
#> year^10 -0.074641489 0.025428484 -2.93535 0.0033317 **
#> year^11 -0.024117334 0.025127362 -0.95980 0.3371540
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = -0.011 Deviance explained = 1.35%
#> -REML = -9870.1 Scale est. = 1 n = 7934
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 9.904385109e+3
#> 3 AIC -1.978277022e+4
#> 4 BIC -1.969204436e+4
#> 5 deviance 7.756093795e+3
#> 6 df.residual 7.922 e+3
#> 7 nobs 7.93400 e+3
#> 8 adj.r.squared -1.096589072e-2
#> 9 npar 1.2 e+1
#>
#> ── Model B ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(16.45)
#> Link function: logit
#>
#> Formula:
#> mbepr_beipr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.201794018 0.004008320 -549.30597 < 2.22e-16 ***
#> year.L 0.040093785 0.013924671 2.87933 0.00398515 **
#> year.Q -0.083392401 0.014042704 -5.93849 2.8767e-09 ***
#> year.C -0.011116822 0.013971517 -0.79568 0.42621951
#> year^4 -0.072295526 0.013891383 -5.20434 1.9468e-07 ***
#> year^5 0.112196244 0.013857588 8.09638 5.6621e-16 ***
#> year^6 -0.053673556 0.013822192 -3.88314 0.00010311 ***
#> year^7 -0.026248013 0.013783413 -1.90432 0.05686867 .
#> year^8 0.054572752 0.013781906 3.95974 7.5032e-05 ***
#> year^9 -0.002179925 0.013824727 -0.15768 0.87470654
#> year^10 -0.010776896 0.013886529 -0.77607 0.43770862
#> year^11 0.029660260 0.013948448 2.12642 0.03346829 *
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = -0.00237 Deviance explained = 0.56%
#> -REML = -44226 Scale est. = 1 n = 31734
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 4.426792248e+4
#> 3 AIC -8.850984496e+4
#> 4 BIC -8.840109809e+4
#> 5 deviance 3.182959169e+4
#> 6 df.residual 3.1722 e+4
#> 7 nobs 3.1734 e+4
#> 8 adj.r.squared -2.365279760e-3
#> 9 npar 1.2 e+1
#>
#> ── Model C ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(32.314)
#> Link function: logit
#>
#> Formula:
#> mbepr_beipr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -1.7748564177 0.0033447160 -530.64488 < 2.22e-16 ***
#> year.L -0.2594420089 0.0115120249 -22.53661 < 2.22e-16 ***
#> year.Q 0.1363862197 0.0115958679 11.76162 < 2.22e-16 ***
#> year.C 0.0012775965 0.0115719081 0.11041 0.91208819
#> year^4 -0.0548553810 0.0115527519 -4.74825 0.00000205182 ***
#> year^5 0.0443979132 0.0115655057 3.83882 0.00012363 ***
#> year^6 -0.0231459262 0.0115222410 -2.00880 0.04455790 *
#> year^7 -0.0104135840 0.0115768225 -0.89952 0.36837572
#> year^8 0.0237630550 0.0115831063 2.05153 0.04021565 *
#> year^9 0.0199901948 0.0115759610 1.72687 0.08419078 .
#> year^10 -0.0617533698 0.0116776235 -5.28818 0.00000012354 ***
#> year^11 0.0007588868 0.0117154010 0.06478 0.94835167
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = 0.0434 Deviance explained = 3.53%
#> -REML = -28926 Scale est. = 1 n = 20324
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 4.335752981e-2 weak cohen1988
#> 2 SE 2.794039468e-3 <NA> <NA>
#> 3 Lower CI 3.788131308e-2 weak cohen1988
#> 4 Upper CI 4.883374654e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 2.897004590e+4
#> 3 AIC -5.791409181e+4
#> 4 BIC -5.781113756e+4
#> 5 deviance 1.982049212e+4
#> 6 df.residual 2.03120000 e+4
#> 7 nobs 2.0324 e+4
#> 8 adj.r.squared 4.335752981e-2
#> 9 npar 1.2 e+1
#>
#> ── Model D ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(24.343)
#> Link function: logit
#>
#> Formula:
#> mbepr_beipr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -1.258354871 0.008929517 -140.92082 < 2.22e-16 ***
#> year.L -0.345509238 0.030979054 -11.15300 < 2.22e-16 ***
#> year.Q 0.111788551 0.031051612 3.60009 0.00031811 ***
#> year.C 0.034028105 0.031098416 1.09421 0.27386419
#> year^4 -0.025903944 0.030851767 -0.83963 0.40111816
#> year^5 0.051005021 0.030976997 1.64655 0.09965160 .
#> year^6 -0.079249591 0.030792775 -2.57364 0.01006342 *
#> year^7 -0.005113017 0.030865679 -0.16565 0.86842941
#> year^8 0.071840113 0.030835764 2.32977 0.01981853 *
#> year^9 0.027230290 0.030836002 0.88307 0.37719947
#> year^10 -0.073558247 0.031130417 -2.36291 0.01813227 *
#> year^11 -0.006569161 0.030839502 -0.21301 0.83131819
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = 0.0573 Deviance explained = 5.65%
#> -REML = -3037.9 Scale est. = 1 n = 2770
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 5.729349284e-2 weak cohen1988
#> 2 SE 8.563879749e-3 <NA> <NA>
#> 3 Lower CI 4.050859696e-2 weak cohen1988
#> 4 Upper CI 7.407838871e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 3.069860234e+3
#> 3 AIC -6.113720467e+3
#> 4 BIC -6.036674633e+3
#> 5 deviance 2.685543298e+3
#> 6 df.residual 2.758 e+3
#> 7 nobs 2.77 e+3
#> 8 adj.r.squared 5.729349284e-2
#> 9 npar 1.2 e+1Code
mbepr_beipr_gam_5_by_misfs |>
summarise_coefs_misfs() |>
md_named_tibble()mbepr_beipr_gam_5_by_misfs model.
| A | B | C | D | |
|---|---|---|---|---|
| [Mean] | -0.1598945925 | -0.1854128428 | -0.1631577351 | -0.1248638324 |
| (Intercept) | -1.9278009775 | -2.2017940179 | -1.7748564177 | -1.2583548712 |
| year.L | 0.1550499540 | 0.0400937851 | -0.2594420089 | -0.3455092381 |
| year.Q | -0.0343962737 | -0.0833924014 | 0.1363862197 | 0.1117885509 |
| year.C | -0.0060368785 | -0.0111168219 | 0.0012775965 | 0.0340281054 |
| year^4 | -0.0483527776 | -0.0722955259 | -0.0548553810 | -0.0259039438 |
| year^5 | 0.1444454242 | 0.1121962443 | 0.0443979132 | 0.0510050208 |
| year^6 | -0.1040621684 | -0.0536735555 | -0.0231459262 | -0.0792495910 |
| year^7 | -0.0409254671 | -0.0262480125 | -0.0104135840 | -0.0051130169 |
| year^8 | 0.0480764968 | 0.0545727522 | 0.0237630550 | 0.0718401134 |
| year^9 | -0.0059736197 | -0.0021799254 | 0.0199901948 | 0.0272302901 |
| year^10 | -0.0746414893 | -0.0107768958 | -0.0617533698 | -0.0735582472 |
| year^11 | -0.0241173338 | 0.0296602605 | 0.0007588868 | -0.0065691607 |
Source: Created by the authors.
Code
data |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam_misfs(
gam_models = mbepr_beipr_gam_5_by_misfs,
type = 5,
x_label = "Years",
y_label = "Predicted probability of MBEPR & BEIPR"
)
#> Warning: Removed 12 rows containing missing values or values outside the scale range
#> (`geom_line()`).
#> Warning in max(ids, na.rm = TRUE): no non-missing arguments to max;
#> returning -Infmbepr_beipr_gam_5_by_misfs model. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
Code
maper_gam_5_by_misfs <-
data |>
gam_misfs(maper ~ year)data |>
summarise_gam_misfs(maper_gam_5_by_misfs)
#>
#> ── Model A ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(23.761)
#> Link function: logit
#>
#> Formula:
#> maper ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.530069222 0.009802718 -360.11128 < 2.22e-16 ***
#> year.L 0.104598923 0.034445367 3.03666 0.00239214 **
#> year.Q -0.194940662 0.034505042 -5.64963 0.00000001608 ***
#> year.C -0.069618293 0.034281636 -2.03078 0.04227781 *
#> year^4 -0.112521422 0.034064505 -3.30319 0.00095593 ***
#> year^5 0.075751354 0.034155401 2.21784 0.02656547 *
#> year^6 0.049211214 0.033939964 1.44995 0.14707276
#> year^7 0.002841143 0.033756387 0.08417 0.93292437
#> year^8 0.134923449 0.033567360 4.01948 0.00005832586 ***
#> year^9 0.004377093 0.033514215 0.13060 0.89608852
#> year^10 -0.033243415 0.033703404 -0.98635 0.32396049
#> year^11 -0.019870002 0.033581458 -0.59170 0.55405443
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = -0.0079 Deviance explained = 0.957%
#> -REML = -20716 Scale est. = 1 n = 7934
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 2.074635089e+4
#> 3 AIC -4.146670177e+4
#> 4 BIC -4.137597591e+4
#> 5 deviance 8.433850322e+3
#> 6 df.residual 7.922 e+3
#> 7 nobs 7.93400 e+3
#> 8 adj.r.squared -7.903895660e-3
#> 9 npar 1.2 e+1
#>
#> ── Model B ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(23.009)
#> Link function: logit
#>
#> Formula:
#> maper ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.947715665 0.005230480 -754.75214 < 2.22e-16 ***
#> year.L 0.087036958 0.018122175 4.80279 0.00000156471910 ***
#> year.Q -0.113028621 0.018263601 -6.18874 0.00000000060648 ***
#> year.C -0.105741910 0.018137515 -5.83001 0.00000000554237 ***
#> year^4 -0.107411419 0.018126852 -5.92554 0.00000000311270 ***
#> year^5 0.079974056 0.018101738 4.41803 0.00000996036822 ***
#> year^6 0.018644792 0.018088259 1.03077 0.3026498
#> year^7 0.047323466 0.018029506 2.62478 0.0086705 **
#> year^8 0.092256007 0.018013711 5.12143 0.00000030322303 ***
#> year^9 -0.005596113 0.018048568 -0.31006 0.7565164
#> year^10 -0.003568097 0.018101221 -0.19712 0.8437343
#> year^11 0.009635605 0.018272946 0.52732 0.5979746
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = -0.00248 Deviance explained = 0.544%
#> -REML = -1.0446e+05 Scale est. = 1 n = 31734
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 1.044996352e+5
#> 3 AIC -2.089732704e+5
#> 4 BIC -2.088645236e+5
#> 5 deviance 3.427644493e+4
#> 6 df.residual 3.1722 e+4
#> 7 nobs 3.1734 e+4
#> 8 adj.r.squared -2.481012795e-3
#> 9 npar 1.2 e+1
#>
#> ── Model C ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(51.613)
#> Link function: logit
#>
#> Formula:
#> maper ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.400622395 0.004764848 -713.68955 < 2.22e-16 ***
#> year.L -0.156051988 0.016747421 -9.31797 < 2.22e-16 ***
#> year.Q -0.128726095 0.016714329 -7.70154 0.000000000000013443 ***
#> year.C -0.005769232 0.016587436 -0.34781 0.7279849
#> year^4 -0.024311829 0.016575313 -1.46675 0.1424443
#> year^5 0.072274727 0.016663513 4.33730 0.000014424083339625 ***
#> year^6 0.049416716 0.016514786 2.99227 0.0027691 **
#> year^7 0.010033851 0.016506714 0.60786 0.5432771
#> year^8 0.074491098 0.016371442 4.55006 0.000005362977646052 ***
#> year^9 -0.014569827 0.016226118 -0.89792 0.3692259
#> year^10 -0.086108370 0.016350984 -5.26625 0.000000139238658588 ***
#> year^11 0.035871456 0.016297906 2.20099 0.0277370 *
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = 0.0109 Deviance explained = 1.15%
#> -REML = -50950 Scale est. = 1 n = 20324
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 1.094496673e-2 very weak (negligible) cohen1988
#> 2 SE 1.451370507e-3 <NA> <NA>
#> 3 Lower CI 8.100332809e-3 very weak (negligible) cohen1988
#> 4 Upper CI 1.378960065e-2 very weak (negligible) cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 5.098980161e+4
#> 3 AIC -1.019536032e+5
#> 4 BIC -1.018506490e+5
#> 5 deviance 2.004505690e+4
#> 6 df.residual 2.03120000 e+4
#> 7 nobs 2.0324 e+4
#> 8 adj.r.squared 1.094496673e-2
#> 9 npar 1.2 e+1
#>
#> ── Model D ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(84.23)
#> Link function: logit
#>
#> Formula:
#> maper ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.515374052 0.011174422 -314.59113 < 2.22e-16 ***
#> year.L -0.230141752 0.039373090 -5.84515 0.000000005061 ***
#> year.Q -0.094313845 0.039229772 -2.40414 0.016211 *
#> year.C -0.114018442 0.039109754 -2.91535 0.003553 **
#> year^4 -0.003614870 0.038856951 -0.09303 0.925880
#> year^5 0.094367111 0.039007013 2.41923 0.015553 *
#> year^6 -0.009984777 0.038729265 -0.25781 0.796554
#> year^7 0.057408694 0.038592128 1.48758 0.136863
#> year^8 0.057557812 0.038355782 1.50063 0.133451
#> year^9 -0.029429933 0.038200427 -0.77041 0.441058
#> year^10 -0.036098574 0.038367993 -0.94085 0.346781
#> year^11 0.039762754 0.037953787 1.04766 0.294794
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = 0.0202 Deviance explained = 2.23%
#> -REML = -7541 Scale est. = 1 n = 2770
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 2.021475971e-2 weak cohen1988
#> 2 SE 5.286966888e-3 <NA> <NA>
#> 3 Lower CI 9.852495026e-3 very weak (negligible) cohen1988
#> 4 Upper CI 3.057702440e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 7.570286498e+3
#> 3 AIC -1.511457300e+4
#> 4 BIC -1.503752716e+4
#> 5 deviance 2.705752165e+3
#> 6 df.residual 2.758 e+3
#> 7 nobs 2.77 e+3
#> 8 adj.r.squared 2.021475971e-2
#> 9 npar 1.2 e+1Code
maper_gam_5_by_misfs |>
summarise_coefs_misfs() |>
md_named_tibble()maper_gam_5_by_misfs model.
| A | B | C | D | |
|---|---|---|---|---|
| [Mean] | -0.2990466532 | -0.3290159117 | -0.2978393239 | -0.3153233228 |
| (Intercept) | -3.5300692218 | -3.9477156646 | -3.4006223949 | -3.5153740522 |
| year.L | 0.1045989226 | 0.0870369581 | -0.1560519880 | -0.2301417517 |
| year.Q | -0.1949406618 | -0.1130286207 | -0.1287260955 | -0.0943138451 |
| year.C | -0.0696182930 | -0.1057419100 | -0.0057692315 | -0.1140184421 |
| year^4 | -0.1125214220 | -0.1074114192 | -0.0243118286 | -0.0036148700 |
| year^5 | 0.0757513539 | 0.0799740560 | 0.0722747273 | 0.0943671110 |
| year^6 | 0.0492112142 | 0.0186447919 | 0.0494167162 | -0.0099847771 |
| year^7 | 0.0028411433 | 0.0473234656 | 0.0100338509 | 0.0574086938 |
| year^8 | 0.1349234490 | 0.0922560068 | 0.0744910981 | 0.0575578122 |
| year^9 | 0.0043770931 | -0.0055961128 | -0.0145698267 | -0.0294299328 |
| year^10 | -0.0332434147 | -0.0035680971 | -0.0861083702 | -0.0360985736 |
| year^11 | -0.0198700017 | 0.0096356051 | 0.0358714562 | 0.0397627537 |
Source: Created by the authors.
Code
data |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam_misfs(
gam_models = maper_gam_5_by_misfs,
type = 5,
x_label = "Years",
y_label = "Predicted probability of MAPER"
)maper_gam_5_by_misfs model. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
Code
mpepr_gam_5_by_misfs <-
data |>
gam_misfs(mpepr ~ year)data |>
summarise_gam_misfs(mpepr_gam_5_by_misfs)
#>
#> ── Model A ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(31.103)
#> Link function: logit
#>
#> Formula:
#> mpepr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.418001960 0.008985228 -380.40237 < 2.22e-16 ***
#> year.L 0.303094333 0.031609890 9.58859 < 2.22e-16 ***
#> year.Q -0.158190676 0.031750384 -4.98232 0.00000062825 ***
#> year.C -0.097470279 0.031462320 -3.09800 0.00194831 **
#> year^4 -0.138041366 0.031282628 -4.41272 0.00001020817 ***
#> year^5 -0.009086991 0.031237449 -0.29090 0.77112738
#> year^6 0.049991213 0.031092736 1.60781 0.10787678
#> year^7 -0.038833115 0.030857266 -1.25848 0.20821983
#> year^8 0.059640021 0.030709881 1.94205 0.05213146 .
#> year^9 -0.024743805 0.030708151 -0.80577 0.42037363
#> year^10 0.016476066 0.030781723 0.53525 0.59247365
#> year^11 0.119592933 0.030868570 3.87426 0.00010695 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = -0.0362 Deviance explained = 2.05%
#> -REML = -19440 Scale est. = 1 n = 7934
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 1.947212870e+4
#> 3 AIC -3.891825739e+4
#> 4 BIC -3.882753153e+4
#> 5 deviance 8.411778743e+3
#> 6 df.residual 7.922 e+3
#> 7 nobs 7.93400 e+3
#> 8 adj.r.squared -3.620918501e-2
#> 9 npar 1.2 e+1
#>
#> ── Model B ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(25.906)
#> Link function: logit
#>
#> Formula:
#> mpepr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.738960964 0.004992705 -748.88475 < 2.22e-16 ***
#> year.L 0.221077589 0.017235399 12.82695 < 2.22e-16 ***
#> year.Q 0.012081960 0.017484799 0.69100 0.48956685
#> year.C -0.082749263 0.017281986 -4.78818 0.000001683 ***
#> year^4 -0.215515173 0.017280621 -12.47149 < 2.22e-16 ***
#> year^5 0.039394268 0.017260073 2.28239 0.02246616 *
#> year^6 0.069864307 0.017249593 4.05020 0.000051174 ***
#> year^7 0.059107063 0.017159763 3.44452 0.00057208 ***
#> year^8 0.075172297 0.017141556 4.38538 0.000011578 ***
#> year^9 0.007909703 0.017212102 0.45954 0.64584421
#> year^10 0.017543664 0.017317823 1.01304 0.31104060
#> year^11 0.008739832 0.017618222 0.49607 0.61984660
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = -0.00743 Deviance explained = 1.15%
#> -REML = -90886 Scale est. = 1 n = 31734
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 9.092481949e+4
#> 3 AIC -1.818236390e+5
#> 4 BIC -1.817148921e+5
#> 5 deviance 3.487532075e+4
#> 6 df.residual 3.1722 e+4
#> 7 nobs 3.1734 e+4
#> 8 adj.r.squared -7.427616944e-3
#> 9 npar 1.2 e+1
#>
#> ── Model C ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(87.973)
#> Link function: logit
#>
#> Formula:
#> mpepr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.329260365 0.003776245 -881.63259 < 2.22e-16 ***
#> year.L -0.066944070 0.013287304 -5.03820 0.00000046994 ***
#> year.Q -0.119293498 0.013280073 -8.98289 < 2.22e-16 ***
#> year.C 0.021973098 0.013169676 1.66846 0.0952241 .
#> year^4 -0.038821997 0.013191626 -2.94293 0.0032512 **
#> year^5 -0.020191074 0.013118969 -1.53907 0.1237860
#> year^6 0.036234449 0.013094189 2.76722 0.0056537 **
#> year^7 -0.002668151 0.013035156 -0.20469 0.8378152
#> year^8 -0.016756343 0.012982576 -1.29068 0.1968149
#> year^9 -0.033482543 0.012924629 -2.59060 0.0095809 **
#> year^10 0.004664769 0.012853677 0.36291 0.7166697
#> year^11 0.006941334 0.012948368 0.53608 0.5919047
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = 0.00809 Deviance explained = 0.688%
#> -REML = -53469 Scale est. = 1 n = 20324
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 8.093105311e-3 very weak (negligible) cohen1988
#> 2 SE 1.251639090e-3 <NA> <NA>
#> 3 Lower CI 5.639937773e-3 very weak (negligible) cohen1988
#> 4 Upper CI 1.054627285e-2 very weak (negligible) cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 5.351150485e+4
#> 3 AIC -1.069970097e+5
#> 4 BIC -1.068940554e+5
#> 5 deviance 2.017974368e+4
#> 6 df.residual 2.03120000 e+4
#> 7 nobs 2.0324 e+4
#> 8 adj.r.squared 8.093105311e-3
#> 9 npar 1.2 e+1
#>
#> ── Model D ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(117.623)
#> Link function: logit
#>
#> Formula:
#> mpepr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.317347903 0.008989679 -369.01738 < 2.22e-16 ***
#> year.L -0.100166486 0.031690452 -3.16078 0.0015735 **
#> year.Q -0.093514337 0.031543235 -2.96464 0.0030304 **
#> year.C -0.035982148 0.031531742 -1.14114 0.2538115
#> year^4 0.006963582 0.031279783 0.22262 0.8238294
#> year^5 0.058011246 0.031279652 1.85460 0.0636534 .
#> year^6 -0.035862589 0.031206635 -1.14920 0.2504745
#> year^7 0.048180826 0.030966098 1.55592 0.1197267
#> year^8 0.036398244 0.030863216 1.17934 0.2382626
#> year^9 -0.083403748 0.030898803 -2.69926 0.0069495 **
#> year^10 0.018230570 0.030806937 0.59177 0.5540057
#> year^11 0.002568151 0.030463825 0.08430 0.9328166
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = 0.00546 Deviance explained = 1.33%
#> -REML = -7565.5 Scale est. = 1 n = 2770
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 5.458795517e-3 very weak (negligible) cohen1988
#> 2 SE 2.788769371e-3 <NA> <NA>
#> 3 Lower CI -7.092011279e-6 no effect cohen1988
#> 4 Upper CI 1.092468305e-2 very weak (negligible) cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 7.597365316e+3
#> 3 AIC -1.516873063e+4
#> 4 BIC -1.509168480e+4
#> 5 deviance 2.718494668e+3
#> 6 df.residual 2.758 e+3
#> 7 nobs 2.77 e+3
#> 8 adj.r.squared 5.458795517e-3
#> 9 npar 1.2 e+1Code
mpepr_gam_5_by_misfs |>
summarise_coefs_misfs() |>
md_named_tibble()mpepr_gam_5_by_misfs model.
| A | B | C | D | |
|---|---|---|---|---|
| [Mean] | -0.2779644688 | -0.2938612265 | -0.2964670326 | -0.2913270493 |
| (Intercept) | -3.4180019602 | -3.7389609638 | -3.3292603651 | -3.3173479030 |
| year.L | 0.3030943327 | 0.2210775893 | -0.0669440696 | -0.1001664860 |
| year.Q | -0.1581906756 | 0.0120819597 | -0.1192934981 | -0.0935143371 |
| year.C | -0.0974702788 | -0.0827492634 | 0.0219730983 | -0.0359821476 |
| year^4 | -0.1380413663 | -0.2155151734 | -0.0388219970 | 0.0069635820 |
| year^5 | -0.0090869910 | 0.0393942678 | -0.0201910740 | 0.0580112458 |
| year^6 | 0.0499912135 | 0.0698643068 | 0.0362344492 | -0.0358625885 |
| year^7 | -0.0388331147 | 0.0591070634 | -0.0026681514 | 0.0481808261 |
| year^8 | 0.0596400206 | 0.0751722973 | -0.0167563433 | 0.0363982444 |
| year^9 | -0.0247438051 | 0.0079097026 | -0.0334825426 | -0.0834037479 |
| year^10 | 0.0164760660 | 0.0175436644 | 0.0046647693 | 0.0182305701 |
| year^11 | 0.1195929332 | 0.0087398317 | 0.0069413337 | 0.0025681507 |
Source: Created by the authors.
Code
data |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam_misfs(
gam_models = mpepr_gam_5_by_misfs,
type = 5,
x_label = "Years",
y_label = "Predicted probability of MPEPR"
)mpepr_gam_5_by_misfs model. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
Code
maper_mpepr_gam_5_by_misfs <-
data |>
gam_misfs(maper_mpepr ~ year)data |>
summarise_gam_misfs(maper_mpepr_gam_5_by_misfs)
#>
#> ── Model A ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(23.539)
#> Link function: logit
#>
#> Formula:
#> maper_mpepr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.739534862 0.008193872 -334.33946 < 2.22e-16 ***
#> year.L 0.082363380 0.028987838 2.84131 0.0044929 **
#> year.Q -0.220214939 0.028964569 -7.60291 0.000000000000028955 ***
#> year.C -0.071155219 0.028714511 -2.47802 0.0132113 *
#> year^4 -0.067622213 0.028554304 -2.36820 0.0178750 *
#> year^5 -0.004810695 0.028628284 -0.16804 0.8665519
#> year^6 0.061860888 0.028446118 2.17467 0.0296549 *
#> year^7 -0.005878489 0.028196928 -0.20848 0.8348544
#> year^8 0.094310981 0.027973611 3.37143 0.0007478 ***
#> year^9 -0.025048934 0.027892481 -0.89805 0.3691571
#> year^10 -0.003939729 0.027970941 -0.14085 0.8879878
#> year^11 0.038761967 0.027867424 1.39094 0.1642431
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = -0.0105 Deviance explained = 1.21%
#> -REML = -14639 Scale est. = 1 n = 7934
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 1.467225123e+4
#> 3 AIC -2.931850246e+4
#> 4 BIC -2.922777659e+4
#> 5 deviance 8.012581771e+3
#> 6 df.residual 7.922 e+3
#> 7 nobs 7.93400 e+3
#> 8 adj.r.squared -1.046017779e-2
#> 9 npar 1.2 e+1
#>
#> ── Model B ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(18.318)
#> Link function: logit
#>
#> Formula:
#> maper_mpepr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.124703269 0.004814081 -649.07572 < 2.22e-16 ***
#> year.L 0.100863495 0.016648945 6.05825 0.00000000137609 ***
#> year.Q -0.028135499 0.016892394 -1.66557 0.095799 .
#> year.C -0.105013255 0.016687318 -6.29300 0.00000000031139 ***
#> year^4 -0.203844570 0.016660694 -12.23506 < 2.22e-16 ***
#> year^5 0.065707778 0.016659323 3.94420 0.00008006532378 ***
#> year^6 0.055786070 0.016640398 3.35245 0.000801 ***
#> year^7 0.079608090 0.016524969 4.81744 0.00000145409931 ***
#> year^8 0.099892126 0.016494522 6.05608 0.00000000139480 ***
#> year^9 0.003558448 0.016575211 0.21468 0.830013
#> year^10 0.022954355 0.016691884 1.37518 0.169075
#> year^11 -0.004565760 0.016959601 -0.26921 0.787765
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = -0.00293 Deviance explained = 0.958%
#> -REML = -69446 Scale est. = 1 n = 31734
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 6.948485640e+4
#> 3 AIC -1.389437128e+5
#> 4 BIC -1.388349659e+5
#> 5 deviance 3.380460192e+4
#> 6 df.residual 3.1722 e+4
#> 7 nobs 3.1734 e+4
#> 8 adj.r.squared -2.933590148e-3
#> 9 npar 1.2 e+1
#>
#> ── Model C ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(47.029)
#> Link function: logit
#>
#> Formula:
#> maper_mpepr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.63424132 0.00379491 -694.15115 < 2.22e-16 ***
#> year.L -0.19388264 0.01331919 -14.55664 < 2.22e-16 ***
#> year.Q -0.09853273 0.01329936 -7.40883 0.00000000000012742 ***
#> year.C 0.01465584 0.01319804 1.11046 0.26680250
#> year^4 -0.02233616 0.01322368 -1.68910 0.09119974 .
#> year^5 0.01495000 0.01321981 1.13088 0.25810634
#> year^6 0.04709845 0.01317008 3.57617 0.00034866 ***
#> year^7 0.02894606 0.01313051 2.20449 0.02748996 *
#> year^8 0.01641733 0.01305828 1.25724 0.20866850
#> year^9 -0.02147188 0.01298240 -1.65392 0.09814339 .
#> year^10 -0.02379351 0.01297583 -1.83368 0.06670170 .
#> year^11 0.01030478 0.01302273 0.79129 0.42877386
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = 0.0206 Deviance explained = 1.49%
#> -REML = -40561 Scale est. = 1 n = 20324
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 2.062532839e-2 weak cohen1988
#> 2 SE 1.972876581e-3 <NA> <NA>
#> 3 Lower CI 1.675856135e-2 very weak (negligible) cohen1988
#> 4 Upper CI 2.449209544e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 4.060348116e+4
#> 3 AIC -8.118096232e+4
#> 4 BIC -8.107800807e+4
#> 5 deviance 1.989046593e+4
#> 6 df.residual 2.03120000 e+4
#> 7 nobs 2.0324 e+4
#> 8 adj.r.squared 2.062532839e-2
#> 9 npar 1.2 e+1
#>
#> ── Model D ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(61.083)
#> Link function: logit
#>
#> Formula:
#> maper_mpepr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.684646160 0.009359123 -286.84803 < 2.22e-16 ***
#> year.L -0.210167823 0.032975651 -6.37342 0.00000000018485 ***
#> year.Q -0.092082220 0.032836320 -2.80428 0.0050429 **
#> year.C -0.059427053 0.032764265 -1.81378 0.0697121 .
#> year^4 0.003131789 0.032551557 0.09621 0.9233537
#> year^5 0.064703168 0.032619275 1.98359 0.0473019 *
#> year^6 -0.016697182 0.032525210 -0.51336 0.6076987
#> year^7 0.064299439 0.032259521 1.99319 0.0462404 *
#> year^8 0.050280508 0.032108191 1.56597 0.1173553
#> year^9 -0.069140052 0.032116659 -2.15278 0.0313361 *
#> year^10 0.014253882 0.032077071 0.44436 0.6567797
#> year^11 0.011076706 0.031774920 0.34860 0.7273904
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = 0.0212 Deviance explained = 2.44%
#> -REML = -5871.2 Scale est. = 1 n = 2770
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 2.117818155e-2 weak cohen1988
#> 2 SE 5.406166049e-3 <NA> <NA>
#> 3 Lower CI 1.058229080e-2 very weak (negligible) cohen1988
#> 4 Upper CI 3.177407230e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 5.902573955e+3
#> 3 AIC -1.177914791e+4
#> 4 BIC -1.170210208e+4
#> 5 deviance 2.706397613e+3
#> 6 df.residual 2.758 e+3
#> 7 nobs 2.77 e+3
#> 8 adj.r.squared 2.117818155e-2
#> 9 npar 1.2 e+1Code
maper_mpepr_gam_5_by_misfs |>
summarise_coefs_misfs() |>
md_named_tibble()maper_mpepr_gam_5_by_misfs model.
| A | B | C | D | |
|---|---|---|---|---|
| [Mean] | -0.2384089887 | -0.2531576660 | -0.2384904811 | -0.2437012497 |
| (Intercept) | -2.7395348624 | -3.1247032688 | -2.6342413182 | -2.6846461599 |
| year.L | 0.0823633804 | 0.1008634953 | -0.1938826392 | -0.2101678227 |
| year.Q | -0.2202149387 | -0.0281354988 | -0.0985327352 | -0.0920822200 |
| year.C | -0.0711552193 | -0.1050132546 | 0.0146558429 | -0.0594270534 |
| year^4 | -0.0676222131 | -0.2038445702 | -0.0223361557 | 0.0031317894 |
| year^5 | -0.0048106947 | 0.0657077777 | 0.0149499977 | 0.0647031685 |
| year^6 | 0.0618608881 | 0.0557860702 | 0.0470984492 | -0.0166971821 |
| year^7 | -0.0058784895 | 0.0796080896 | 0.0289460634 | 0.0642994388 |
| year^8 | 0.0943109810 | 0.0998921256 | 0.0164173331 | 0.0502805084 |
| year^9 | -0.0250489340 | 0.0035584476 | -0.0214718792 | -0.0691400520 |
| year^10 | -0.0039397290 | 0.0229543549 | -0.0237935069 | 0.0142538824 |
| year^11 | 0.0387619668 | -0.0045657601 | 0.0103047747 | 0.0110767063 |
Source: Created by the authors.
Code
data |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam_misfs(
gam_models = maper_mpepr_gam_5_by_misfs,
type = 5,
x_label = "Years",
y_label = "Predicted probability of MAPER & MPEPR"
)maper_mpepr_gam_5_by_misfs model. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
By year (Unordered)
In this model, the year variable is treated as a unordered categorical variable.
dplyr::mutate(data, year = factor(year, ordered = FALSE)) |>
summarise_gam_misfs(mbepr_gam_6_by_misfs)
#>
#> ── Model A ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(18.537)
#> Link function: logit
#>
#> Formula:
#> mbepr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.09424687 0.03427877 -90.26715 < 2.22e-16 ***
#> year2009 0.35266775 0.04594284 7.67623 0.000000000000016384 ***
#> year2010 0.37775186 0.04580514 8.24693 < 2.22e-16 ***
#> year2011 0.23380479 0.04645506 5.03292 0.000000483054025019 ***
#> year2012 0.17344883 0.04675819 3.70949 0.00020768 ***
#> year2013 0.32506147 0.04600019 7.06653 0.000000000001588614 ***
#> year2014 0.45806746 0.04531048 10.10953 < 2.22e-16 ***
#> year2015 0.34842813 0.04585668 7.59820 0.000000000000030028 ***
#> year2016 0.48081092 0.04530151 10.61357 < 2.22e-16 ***
#> year2017 0.35239697 0.04594416 7.67011 0.000000000000017184 ***
#> year2018 0.41602966 0.04561816 9.11983 < 2.22e-16 ***
#> year2019 0.40761286 0.04556986 8.94479 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = -0.0203 Deviance explained = 2.47%
#> -REML = -14556 Scale est. = 1 n = 7934
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 1.458696428e+4
#> 3 AIC -2.914792856e+4
#> 4 BIC -2.905720269e+4
#> 5 deviance 8.119205011e+3
#> 6 df.residual 7.922 e+3
#> 7 nobs 7.93400 e+3
#> 8 adj.r.squared -2.027317837e-2
#> 9 npar 1.2 e+1
#>
#> ── Model B ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(16.507)
#> Link function: logit
#>
#> Formula:
#> mbepr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.27874915 0.01784467 -183.73827 < 2.22e-16 ***
#> year2009 0.21482871 0.02452461 8.75972 < 2.22e-16 ***
#> year2010 0.24718735 0.02439970 10.13075 < 2.22e-16 ***
#> year2011 0.16598082 0.02461120 6.74412 0.000000000015396 ***
#> year2012 0.16136986 0.02463144 6.55138 0.000000000057009 ***
#> year2013 0.25333422 0.02467987 10.26481 < 2.22e-16 ***
#> year2014 0.29507924 0.02457929 12.00520 < 2.22e-16 ***
#> year2015 0.26164151 0.02452007 10.67050 < 2.22e-16 ***
#> year2016 0.29456981 0.02435031 12.09717 < 2.22e-16 ***
#> year2017 0.25769537 0.02443079 10.54797 < 2.22e-16 ***
#> year2018 0.21090578 0.02443018 8.63300 < 2.22e-16 ***
#> year2019 0.16330978 0.02446471 6.67532 0.000000000024669 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = -0.00456 Deviance explained = 0.764%
#> -REML = -68043 Scale est. = 1 n = 31734
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 6.808076769e+4
#> 3 AIC -1.361355354e+5
#> 4 BIC -1.360267885e+5
#> 5 deviance 3.347652301e+4
#> 6 df.residual 3.1722 e+4
#> 7 nobs 3.1734 e+4
#> 8 adj.r.squared -4.559784873e-3
#> 9 npar 1.2 e+1
#>
#> ── Model C ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(38.489)
#> Link function: logit
#>
#> Formula:
#> mbepr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.499558480 0.013918118 -179.59026 < 2.22e-16 ***
#> year2009 0.037046879 0.019339542 1.91560 0.055416 .
#> year2010 0.008275972 0.019465924 0.42515 0.670726
#> year2011 -0.049400274 0.019628098 -2.51681 0.011842 *
#> year2012 -0.177700784 0.019984739 -8.89182 < 2.22e-16 ***
#> year2013 -0.126004996 0.019933730 -6.32119 2.5955e-10 ***
#> year2014 -0.096231615 0.019786308 -4.86355 1.1530e-06 ***
#> year2015 -0.202062015 0.020140317 -10.03271 < 2.22e-16 ***
#> year2016 -0.105372594 0.019764896 -5.33130 9.7512e-08 ***
#> year2017 -0.158609478 0.019990019 -7.93443 2.1146e-15 ***
#> year2018 -0.184771030 0.020194355 -9.14964 < 2.22e-16 ***
#> year2019 -0.163958341 0.020023947 -8.18811 2.6535e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = 0.0285 Deviance explained = 1.87%
#> -REML = -38671 Scale est. = 1 n = 20324
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 2.851689999e-2 weak cohen1988
#> 2 SE 2.301108092e-3 <NA> <NA>
#> 3 Lower CI 2.400681100e-2 weak cohen1988
#> 4 Upper CI 3.302698897e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 3.871102690e+4
#> 3 AIC -7.739605379e+4
#> 4 BIC -7.729309954e+4
#> 5 deviance 1.976947966e+4
#> 6 df.residual 2.03120000 e+4
#> 7 nobs 2.0324 e+4
#> 8 adj.r.squared 2.851689999e-2
#> 9 npar 1.2 e+1
#>
#> ── Model D ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(35.093)
#> Link function: logit
#>
#> Formula:
#> mbepr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.08278548 0.03440989 -60.52869 < 2.22e-16 ***
#> year2009 0.03529121 0.04785209 0.73751 0.46081461
#> year2010 -0.05957442 0.04833477 -1.23254 0.21774829
#> year2011 -0.12840640 0.04889270 -2.62629 0.00863212 **
#> year2012 -0.32476414 0.05060426 -6.41772 0.00000000013833 ***
#> year2013 -0.16655027 0.04905061 -3.39548 0.00068509 ***
#> year2014 -0.12211249 0.04873553 -2.50562 0.01222385 *
#> year2015 -0.32146788 0.05034339 -6.38550 0.00000000017083 ***
#> year2016 -0.27119000 0.05000667 -5.42308 0.00000005858187 ***
#> year2017 -0.28255052 0.05016444 -5.63249 0.00000001776299 ***
#> year2018 -0.29671761 0.05046571 -5.87959 0.00000000411288 ***
#> year2019 -0.28605072 0.05048667 -5.66587 0.00000001462836 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = 0.0455 Deviance explained = 5.16%
#> -REML = -4658.7 Scale est. = 1 n = 2770
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 4.545270470e-2 weak cohen1988
#> 2 SE 7.723581311e-3 <NA> <NA>
#> 3 Lower CI 3.031476350e-2 weak cohen1988
#> 4 Upper CI 6.059064590e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 4.687741024e+3
#> 3 AIC -9.349482048e+3
#> 4 BIC -9.272436214e+3
#> 5 deviance 2.677966059e+3
#> 6 df.residual 2.758 e+3
#> 7 nobs 2.77 e+3
#> 8 adj.r.squared 4.545270470e-2
#> 9 npar 1.2 e+1Code
mbepr_gam_6_by_misfs |>
summarise_coefs_misfs() |>
md_named_tibble()mbepr_gam_6_by_misfs model.
| A | B | C | D | |
|---|---|---|---|---|
| [Mean] | 0.0693194859 | -0.0627372249 | -0.3098622298 | -0.3589065592 |
| (Intercept) | -3.0942468670 | -3.2787491509 | -2.4995584805 | -2.0827854800 |
| year2009 | 0.3526677517 | 0.2148287090 | 0.0370468786 | 0.0352912122 |
| year2010 | 0.3777518618 | 0.2471873542 | 0.0082759720 | -0.0595744214 |
| year2011 | 0.2338047861 | 0.1659808185 | -0.0494002741 | -0.1284064023 |
| year2012 | 0.1734488271 | 0.1613698600 | -0.1777007842 | -0.3247641446 |
| year2013 | 0.3250614706 | 0.2533342166 | -0.1260049959 | -0.1665502666 |
| year2014 | 0.4580674583 | 0.2950792367 | -0.0962316150 | -0.1221124850 |
| year2015 | 0.3484281296 | 0.2616415114 | -0.2020620149 | -0.3214678849 |
| year2016 | 0.4808109223 | 0.2945698147 | -0.1053725942 | -0.2711899981 |
| year2017 | 0.3523969699 | 0.2576953696 | -0.1586094778 | -0.2825505162 |
| year2018 | 0.4160296607 | 0.2109057842 | -0.1847710302 | -0.2967176079 |
| year2019 | 0.4076128594 | 0.1633097776 | -0.1639583411 | -0.2860507157 |
Source: Created by the authors.
Code
dplyr::mutate(data, year = factor(year, ordered = FALSE)) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam_misfs(
gam_models = mbepr_gam_6_by_misfs,
type = 6,
x_label = "Years",
y_label = "Predicted probability of MBEPR"
)mbepr_gam_6_by_misfs model. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
dplyr::mutate(data, year = factor(year, ordered = FALSE)) |>
summarise_gam_misfs(beipr_gam_6_by_misfs)
#>
#> ── Model A ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(25.127)
#> Link function: logit
#>
#> Formula:
#> beipr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.814996853 0.029385414 -95.79572 < 2.22e-16 ***
#> year2009 0.047204010 0.040554582 1.16396 0.24443923
#> year2010 0.102321228 0.040240677 2.54273 0.01099898 *
#> year2011 0.046227261 0.040502004 1.14136 0.25372123
#> year2012 -0.009950727 0.040823058 -0.24375 0.80742243
#> year2013 0.140876019 0.039977469 3.52389 0.00042527 ***
#> year2014 0.237032038 0.039429416 6.01155 0.000000001837540166 ***
#> year2015 0.265927609 0.039292365 6.76792 0.000000000013064633 ***
#> year2016 0.222930104 0.039596063 5.63011 0.000000018009694788 ***
#> year2017 0.256683443 0.039432108 6.50950 0.000000000075399663 ***
#> year2018 0.334969482 0.039014454 8.58578 < 2.22e-16 ***
#> year2019 0.291545019 0.039160268 7.44492 0.000000000000097004 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = -0.0299 Deviance explained = 2.71%
#> -REML = -14283 Scale est. = 1 n = 7934
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 1.431571354e+4
#> 3 AIC -2.860542709e+4
#> 4 BIC -2.851470122e+4
#> 5 deviance 8.071957558e+3
#> 6 df.residual 7.922 e+3
#> 7 nobs 7.93400 e+3
#> 8 adj.r.squared -2.986476328e-2
#> 9 npar 1.2 e+1
#>
#> ── Model B ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(23.666)
#> Link function: logit
#>
#> Formula:
#> beipr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.99950260 0.01547685 -193.80571 < 2.22e-16 ***
#> year2009 0.14475768 0.02124917 6.81239 0.00000000000959884 ***
#> year2010 0.19377589 0.02106989 9.19681 < 2.22e-16 ***
#> year2011 0.08340476 0.02140071 3.89729 0.00009727491473461 ***
#> year2012 0.03057329 0.02155042 1.41869 0.15599
#> year2013 0.15642915 0.02142306 7.30191 0.00000000000028372 ***
#> year2014 0.15686446 0.02141386 7.32537 0.00000000000023824 ***
#> year2015 0.23925807 0.02107722 11.35150 < 2.22e-16 ***
#> year2016 0.19448747 0.02111164 9.21233 < 2.22e-16 ***
#> year2017 0.23472074 0.02100701 11.17345 < 2.22e-16 ***
#> year2018 0.20006704 0.02101582 9.51983 < 2.22e-16 ***
#> year2019 0.17884706 0.02101990 8.50846 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = -0.0159 Deviance explained = 0.926%
#> -REML = -61292 Scale est. = 1 n = 31734
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 6.133176478e+4
#> 3 AIC -1.226375296e+5
#> 4 BIC -1.225287827e+5
#> 5 deviance 3.310622465e+4
#> 6 df.residual 3.1722 e+4
#> 7 nobs 3.1734 e+4
#> 8 adj.r.squared -1.591864228e-2
#> 9 npar 1.2 e+1
#>
#> ── Model C ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(72.251)
#> Link function: logit
#>
#> Formula:
#> beipr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.38640477 0.01011229 -235.99050 < 2.22e-16 ***
#> year2009 0.01240122 0.01410606 0.87914 0.37932
#> year2010 -0.05868963 0.01431967 -4.09853 4.1578e-05 ***
#> year2011 -0.10144465 0.01441618 -7.03686 1.9662e-12 ***
#> year2012 -0.20262047 0.01464463 -13.83582 < 2.22e-16 ***
#> year2013 -0.14515340 0.01457319 -9.96031 < 2.22e-16 ***
#> year2014 -0.15512159 0.01456849 -10.64775 < 2.22e-16 ***
#> year2015 -0.15588298 0.01455961 -10.70654 < 2.22e-16 ***
#> year2016 -0.18318271 0.01460994 -12.53822 < 2.22e-16 ***
#> year2017 -0.14812384 0.01453951 -10.18768 < 2.22e-16 ***
#> year2018 -0.11299046 0.01451904 -7.78223 7.1258e-15 ***
#> year2019 -0.13869570 0.01452353 -9.54972 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = 0.036 Deviance explained = 2.34%
#> -REML = -42820 Scale est. = 1 n = 20324
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 3.600156273e-2 weak cohen1988
#> 2 SE 2.565592159e-3 <NA> <NA>
#> 3 Lower CI 3.097309450e-2 weak cohen1988
#> 4 Upper CI 4.103003096e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 4.286366655e+4
#> 3 AIC -8.570133310e+4
#> 4 BIC -8.559837885e+4
#> 5 deviance 2.003054550e+4
#> 6 df.residual 2.03120000 e+4
#> 7 nobs 2.0324 e+4
#> 8 adj.r.squared 3.600156273e-2
#> 9 npar 1.2 e+1
#>
#> ── Model D ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(52.212)
#> Link function: logit
#>
#> Formula:
#> beipr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -1.86640997 0.02671057 -69.87533 < 2.22e-16 ***
#> year2009 0.08173551 0.03687128 2.21678 0.02663815 *
#> year2010 0.04524564 0.03689117 1.22646 0.22002464
#> year2011 -0.02904872 0.03733563 -0.77804 0.43654365
#> year2012 -0.09208464 0.03773260 -2.44045 0.01466885 *
#> year2013 -0.04816000 0.03733637 -1.28990 0.19708708
#> year2014 -0.06393338 0.03747366 -1.70609 0.08799159 .
#> year2015 -0.13017766 0.03781844 -3.44217 0.00057706 ***
#> year2016 -0.14931515 0.03802615 -3.92664 0.000086139 ***
#> year2017 -0.11293230 0.03782711 -2.98549 0.00283128 **
#> year2018 -0.10408259 0.03789251 -2.74679 0.00601826 **
#> year2019 -0.11058879 0.03801898 -2.90878 0.00362844 **
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = 0.0327 Deviance explained = 2.94%
#> -REML = -4686.6 Scale est. = 1 n = 2770
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 3.271189059e-2 weak cohen1988
#> 2 SE 6.639724773e-3 <NA> <NA>
#> 3 Lower CI 1.969826917e-2 very weak (negligible) cohen1988
#> 4 Upper CI 4.572551202e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 4.719121470e+3
#> 3 AIC -9.412242941e+3
#> 4 BIC -9.335197107e+3
#> 5 deviance 2.714505806e+3
#> 6 df.residual 2.758 e+3
#> 7 nobs 2.77 e+3
#> 8 adj.r.squared 3.271189059e-2
#> 9 npar 1.2 e+1Code
beipr_gam_6_by_misfs |>
summarise_coefs_misfs() |>
md_named_tibble()beipr_gam_6_by_misfs model.
| A | B | C | D | |
|---|---|---|---|---|
| [Mean] | -0.0732692806 | -0.0988597485 | -0.3146590824 | -0.2149793375 |
| (Intercept) | -2.8149968533 | -2.9995026026 | -2.3864047732 | -1.8664099721 |
| year2009 | 0.0472040103 | 0.1447576844 | 0.0124012174 | 0.0817355101 |
| year2010 | 0.1023212283 | 0.1937758873 | -0.0586896332 | 0.0452456421 |
| year2011 | 0.0462272613 | 0.0834047646 | -0.1014446494 | -0.0290487244 |
| year2012 | -0.0099507266 | 0.0305732904 | -0.2026204683 | -0.0920846360 |
| year2013 | 0.1408760186 | 0.1564291540 | -0.1451534035 | -0.0481600037 |
| year2014 | 0.2370320376 | 0.1568644566 | -0.1551215863 | -0.0639333834 |
| year2015 | 0.2659276085 | 0.2392580691 | -0.1558829841 | -0.1301776573 |
| year2016 | 0.2229301040 | 0.1944874677 | -0.1831827111 | -0.1493151452 |
| year2017 | 0.2566834431 | 0.2347207432 | -0.1481238355 | -0.1129323015 |
| year2018 | 0.3349694817 | 0.2000670429 | -0.1129904588 | -0.1040825865 |
| year2019 | 0.2915450188 | 0.1788470608 | -0.1386957024 | -0.1105887918 |
Source: Created by the authors.
Code
dplyr::mutate(data, year = factor(year, ordered = FALSE)) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam_misfs(
gam_models = beipr_gam_6_by_misfs,
type = 6,
x_label = "Years",
y_label = "Predicted probability of BEIPR"
)beipr_gam_6_by_misfs model. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
dplyr::mutate(data, year = factor(year, ordered = FALSE)) |>
summarise_gam_misfs(mbepr_beipr_gam_6_by_misfs)
#>
#> ── Model A ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(17.202)
#> Link function: logit
#>
#> Formula:
#> mbepr_beipr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.08080565 0.02740893 -75.91707 < 2.22e-16 ***
#> year2009 0.19055073 0.03715369 5.12872 0.0000002917242204 ***
#> year2010 0.15908459 0.03728661 4.26653 0.0000198532878715 ***
#> year2011 0.07512878 0.03764546 1.99569 0.045967 *
#> year2012 0.02408713 0.03790746 0.63542 0.525155
#> year2013 0.15950743 0.03723322 4.28401 0.0000183555587381 ***
#> year2014 0.26091254 0.03673717 7.10214 0.0000000000012284 ***
#> year2015 0.17356083 0.03714285 4.67279 0.0000029713107767 ***
#> year2016 0.21454511 0.03703127 5.79362 0.0000000068885232 ***
#> year2017 0.16408621 0.03727622 4.40190 0.0000107306762664 ***
#> year2018 0.20961319 0.03705370 5.65701 0.0000000154032438 ***
#> year2019 0.20497947 0.03699936 5.54008 0.0000000302331853 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = -0.011 Deviance explained = 1.35%
#> -REML = -9871.3 Scale est. = 1 n = 7934
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 9.904385109e+3
#> 3 AIC -1.978277022e+4
#> 4 BIC -1.969204436e+4
#> 5 deviance 7.756093795e+3
#> 6 df.residual 7.922 e+3
#> 7 nobs 7.93400 e+3
#> 8 adj.r.squared -1.096589072e-2
#> 9 npar 1.2 e+1
#>
#> ── Model B ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(16.45)
#> Link function: logit
#>
#> Formula:
#> mbepr_beipr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.31712574 0.01459629 -158.74759 < 2.22e-16 ***
#> year2009 0.15600119 0.02000904 7.79654 6.3629e-15 ***
#> year2010 0.16915137 0.01992975 8.48738 < 2.22e-16 ***
#> year2011 0.07958637 0.02018918 3.94203 8.0795e-05 ***
#> year2012 0.03616871 0.02030823 1.78099 0.074914 .
#> year2013 0.14323144 0.02023487 7.07845 1.4578e-12 ***
#> year2014 0.16235850 0.02017847 8.04612 8.5458e-16 ***
#> year2015 0.17061424 0.02004920 8.50978 < 2.22e-16 ***
#> year2016 0.13893044 0.02004608 6.93056 4.1919e-12 ***
#> year2017 0.14243165 0.02003915 7.10767 1.1802e-12 ***
#> year2018 0.10490315 0.02005155 5.23167 1.6798e-07 ***
#> year2019 0.08060366 0.02006139 4.01785 5.8731e-05 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = -0.00237 Deviance explained = 0.56%
#> -REML = -44228 Scale est. = 1 n = 31734
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 4.426792248e+4
#> 3 AIC -8.850984496e+4
#> 4 BIC -8.840109809e+4
#> 5 deviance 3.182959169e+4
#> 6 df.residual 3.1722 e+4
#> 7 nobs 3.1734 e+4
#> 8 adj.r.squared -2.365279760e-3
#> 9 npar 1.2 e+1
#>
#> ── Model C ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(32.314)
#> Link function: logit
#>
#> Formula:
#> mbepr_beipr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -1.62203590 0.01128229 -143.76834 < 2.22e-16 ***
#> year2009 0.01927930 0.01573038 1.22561 0.22034559
#> year2010 -0.05501702 0.01593038 -3.45359 0.00055317 ***
#> year2011 -0.09989673 0.01601573 -6.23741 0.00000000044487 ***
#> year2012 -0.22444470 0.01626701 -13.79754 < 2.22e-16 ***
#> year2013 -0.19058010 0.01628383 -11.70364 < 2.22e-16 ***
#> year2014 -0.18134686 0.01622227 -11.17889 < 2.22e-16 ***
#> year2015 -0.24526825 0.01638007 -14.97358 < 2.22e-16 ***
#> year2016 -0.21094895 0.01625574 -12.97689 < 2.22e-16 ***
#> year2017 -0.21671607 0.01630568 -13.29084 < 2.22e-16 ***
#> year2018 -0.21346543 0.01638834 -13.02545 < 2.22e-16 ***
#> year2019 -0.21544144 0.01631477 -13.20530 < 2.22e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = 0.0434 Deviance explained = 3.53%
#> -REML = -28928 Scale est. = 1 n = 20324
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 4.335752981e-2 weak cohen1988
#> 2 SE 2.794039468e-3 <NA> <NA>
#> 3 Lower CI 3.788131308e-2 weak cohen1988
#> 4 Upper CI 4.883374654e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 2.897004590e+4
#> 3 AIC -5.791409181e+4
#> 4 BIC -5.781113756e+4
#> 5 deviance 1.982049212e+4
#> 6 df.residual 2.03120000 e+4
#> 7 nobs 2.0324 e+4
#> 8 adj.r.squared 4.335752981e-2
#> 9 npar 1.2 e+1
#>
#> ── Model D ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(24.343)
#> Link function: logit
#>
#> Formula:
#> mbepr_beipr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -1.09220914 0.03064617 -35.63934 < 2.22e-16 ***
#> year2009 0.04616821 0.04265173 1.08245 0.27905426
#> year2010 -0.03670936 0.04280411 -0.85761 0.39110617
#> year2011 -0.11280096 0.04317714 -2.61252 0.00898785 **
#> year2012 -0.22979138 0.04380484 -5.24580 0.000000155606953 ***
#> year2013 -0.15380095 0.04325058 -3.55604 0.00037648 ***
#> year2014 -0.14568177 0.04325413 -3.36804 0.00075704 ***
#> year2015 -0.29194788 0.04397095 -6.63956 0.000000000031461 ***
#> year2016 -0.28216332 0.04400982 -6.41137 0.000000000144216 ***
#> year2017 -0.26159951 0.04393841 -5.95378 0.000000002620232 ***
#> year2018 -0.26558406 0.04410863 -6.02114 0.000000001731977 ***
#> year2019 -0.25983777 0.04417477 -5.88204 0.000000004052398 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = 0.0573 Deviance explained = 5.65%
#> -REML = -3039.2 Scale est. = 1 n = 2770
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 5.729349284e-2 weak cohen1988
#> 2 SE 8.563879749e-3 <NA> <NA>
#> 3 Lower CI 4.050859696e-2 weak cohen1988
#> 4 Upper CI 7.407838871e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 3.069860234e+3
#> 3 AIC -6.113720467e+3
#> 4 BIC -6.036674633e+3
#> 5 deviance 2.685543298e+3
#> 6 df.residual 2.758 e+3
#> 7 nobs 2.77 e+3
#> 8 adj.r.squared 5.729349284e-2
#> 9 npar 1.2 e+1Code
mbepr_beipr_gam_6_by_misfs |>
summarise_coefs_misfs() |>
md_named_tibble()mbepr_beipr_gam_6_by_misfs model.
| A | B | C | D | |
|---|---|---|---|---|
| [Mean] | -0.0203958017 | -0.0777620861 | -0.2879901788 | -0.2571631576 |
| (Intercept) | -2.0808056463 | -2.3171257437 | -1.6220358970 | -1.0922091421 |
| year2009 | 0.1905507318 | 0.1560011856 | 0.0192793047 | 0.0461682098 |
| year2010 | 0.1590845870 | 0.1691513728 | -0.0550170208 | -0.0367093630 |
| year2011 | 0.0751287833 | 0.0795863688 | -0.0998967255 | -0.1128009579 |
| year2012 | 0.0240871308 | 0.0361687071 | -0.2244446969 | -0.2297913759 |
| year2013 | 0.1595074335 | 0.1432314421 | -0.1905801023 | -0.1538009465 |
| year2014 | 0.2609125365 | 0.1623584957 | -0.1813468627 | -0.1456817711 |
| year2015 | 0.1735608334 | 0.1706142407 | -0.2452682543 | -0.2919478833 |
| year2016 | 0.2145451149 | 0.1389304403 | -0.2109489477 | -0.2821633165 |
| year2017 | 0.1640862149 | 0.1424316464 | -0.2167160681 | -0.2615995078 |
| year2018 | 0.2096131895 | 0.1049031496 | -0.2134654302 | -0.2655840638 |
| year2019 | 0.2049794702 | 0.0806036609 | -0.2154414446 | -0.2598377727 |
Source: Created by the authors.
Code
dplyr::mutate(data, year = factor(year, ordered = FALSE)) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam_misfs(
gam_models = mbepr_beipr_gam_6_by_misfs,
type = 6,
x_label = "Years",
y_label = "Predicted probability of MBEPR & BEIPR"
)
#> Warning: Removed 12 rows containing missing values or values outside the scale range
#> (`geom_line()`).
#> Warning in max(ids, na.rm = TRUE): no non-missing arguments to max;
#> returning -Infmbepr_beipr_gam_6_by_misfs model. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
dplyr::mutate(data, year = factor(year, ordered = FALSE)) |>
summarise_gam_misfs(maper_gam_6_by_misfs)
#>
#> ── Model A ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(23.761)
#> Link function: logit
#>
#> Formula:
#> maper ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.69189376 0.03615554 -102.11142 < 2.22e-16 ***
#> year2009 0.09122742 0.04986873 1.82935 0.06734703 .
#> year2010 0.22634146 0.04929874 4.59122 0.0000044065745 ***
#> year2011 0.14027588 0.04960297 2.82797 0.00468437 **
#> year2012 0.09591483 0.04979698 1.92612 0.05408972 .
#> year2013 0.18389314 0.04940769 3.72195 0.00019769 ***
#> year2014 0.25367268 0.04906371 5.17027 0.0000002337548 ***
#> year2015 0.19574918 0.04932437 3.96861 0.0000722931747 ***
#> year2016 0.27178813 0.04910363 5.53499 0.0000000311244 ***
#> year2017 0.30595451 0.04897093 6.24768 0.0000000004166 ***
#> year2018 0.10464789 0.04979804 2.10145 0.03560184 *
#> year2019 0.07242936 0.04981757 1.45389 0.14597627
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = -0.0079 Deviance explained = 0.957%
#> -REML = -20717 Scale est. = 1 n = 7934
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 2.074635089e+4
#> 3 AIC -4.146670177e+4
#> 4 BIC -4.137597591e+4
#> 5 deviance 8.433850322e+3
#> 6 df.residual 7.922 e+3
#> 7 nobs 7.93400 e+3
#> 8 adj.r.squared -7.903895660e-3
#> 9 npar 1.2 e+1
#>
#> ── Model B ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(23.009)
#> Link function: logit
#>
#> Formula:
#> maper ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -4.05354613 0.01869655 -216.80719 < 2.22e-16 ***
#> year2009 0.09788021 0.02600527 3.76386 0.00016731 ***
#> year2010 0.12848812 0.02589950 4.96103 7.0122e-07 ***
#> year2011 0.04325298 0.02606435 1.65947 0.09702129 .
#> year2012 0.04013462 0.02608028 1.53889 0.12383179
#> year2013 0.12026109 0.02623224 4.58448 4.5512e-06 ***
#> year2014 0.13745562 0.02619691 5.24702 1.5458e-07 ***
#> year2015 0.14778681 0.02603662 5.67611 1.3779e-08 ***
#> year2016 0.20454883 0.02584291 7.91508 2.4709e-15 ***
#> year2017 0.25107458 0.02577241 9.74199 < 2.22e-16 ***
#> year2018 0.06605114 0.02593643 2.54666 0.01087608 *
#> year2019 0.03303157 0.02591281 1.27472 0.20240838
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = -0.00248 Deviance explained = 0.544%
#> -REML = -1.0446e+05 Scale est. = 1 n = 31734
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 1.044996352e+5
#> 3 AIC -2.089732704e+5
#> 4 BIC -2.088645236e+5
#> 5 deviance 3.427644493e+4
#> 6 df.residual 3.1722 e+4
#> 7 nobs 3.1734 e+4
#> 8 adj.r.squared -2.481012795e-3
#> 9 npar 1.2 e+1
#>
#> ── Model C ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(51.613)
#> Link function: logit
#>
#> Formula:
#> maper ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.408513575 0.016886593 -201.84732 < 2.22e-16 ***
#> year2009 0.042954427 0.023451102 1.83166 0.06700221 .
#> year2010 0.096767078 0.023293388 4.15427 0.0000326324264 ***
#> year2011 0.078873109 0.023326080 3.38133 0.00072137 ***
#> year2012 -0.037792157 0.023661468 -1.59720 0.11022057
#> year2013 0.088124473 0.023341460 3.77545 0.00015972 ***
#> year2014 0.045458354 0.023448534 1.93864 0.05254473 .
#> year2015 -0.006662832 0.023624112 -0.28204 0.77791649
#> year2016 0.053338508 0.023360606 2.28327 0.02241462 *
#> year2017 -0.012634456 0.023649633 -0.53423 0.59317911
#> year2018 -0.144093365 0.024273710 -5.93619 0.0000000029172 ***
#> year2019 -0.109638973 0.024029463 -4.56269 0.0000050502521 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = 0.0109 Deviance explained = 1.15%
#> -REML = -50952 Scale est. = 1 n = 20324
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 1.094496673e-2 very weak (negligible) cohen1988
#> 2 SE 1.451370507e-3 <NA> <NA>
#> 3 Lower CI 8.100332809e-3 very weak (negligible) cohen1988
#> 4 Upper CI 1.378960065e-2 very weak (negligible) cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 5.098980161e+4
#> 3 AIC -1.019536032e+5
#> 4 BIC -1.018506490e+5
#> 5 deviance 2.004505690e+4
#> 6 df.residual 2.03120000 e+4
#> 7 nobs 2.0324 e+4
#> 8 adj.r.squared 1.094496673e-2
#> 9 npar 1.2 e+1
#>
#> ── Model D ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(84.23)
#> Link function: logit
#>
#> Formula:
#> maper ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.434525093 0.038704222 -88.73774 < 2.22e-16 ***
#> year2009 0.033982608 0.053795474 0.63170 0.527583
#> year2010 -0.028244284 0.054120830 -0.52187 0.601758
#> year2011 -0.096589965 0.054803074 -1.76249 0.077986 .
#> year2012 -0.117281161 0.055012953 -2.13188 0.033016 *
#> year2013 0.003471375 0.053644187 0.06471 0.948404
#> year2014 -0.053131949 0.054252554 -0.97934 0.327410
#> year2015 -0.065479155 0.054261095 -1.20674 0.227531
#> year2016 -0.042010091 0.054142851 -0.77591 0.437801
#> year2017 -0.095929383 0.054737443 -1.75254 0.079682 .
#> year2018 -0.251238746 0.056535565 -4.44391 0.000008834 ***
#> year2019 -0.257736758 0.056737006 -4.54266 0.000005555 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = 0.0202 Deviance explained = 2.23%
#> -REML = -7542.3 Scale est. = 1 n = 2770
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 2.021475971e-2 weak cohen1988
#> 2 SE 5.286966888e-3 <NA> <NA>
#> 3 Lower CI 9.852495026e-3 very weak (negligible) cohen1988
#> 4 Upper CI 3.057702440e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 7.570286498e+3
#> 3 AIC -1.511457300e+4
#> 4 BIC -1.503752716e+4
#> 5 deviance 2.705752165e+3
#> 6 df.residual 2.758 e+3
#> 7 nobs 2.77 e+3
#> 8 adj.r.squared 2.021475971e-2
#> 9 npar 1.2 e+1Code
maper_gam_6_by_misfs |>
summarise_coefs_misfs() |>
md_named_tibble()maper_gam_6_by_misfs model.
| A | B | C | D | |
|---|---|---|---|---|
| [Mean] | -0.1458332730 | -0.2319650464 | -0.2761516176 | -0.3670593835 |
| (Intercept) | -3.6918937623 | -4.0535461290 | -3.4085135751 | -3.4345250931 |
| year2009 | 0.0912274236 | 0.0978802057 | 0.0429544267 | 0.0339826078 |
| year2010 | 0.2263414641 | 0.1284881180 | 0.0967670777 | -0.0282442836 |
| year2011 | 0.1402758760 | 0.0432529831 | 0.0788731092 | -0.0965899649 |
| year2012 | 0.0959148332 | 0.0401346192 | -0.0377921574 | -0.1172811614 |
| year2013 | 0.1838931362 | 0.1202610933 | 0.0881244725 | 0.0034713755 |
| year2014 | 0.2536726770 | 0.1374556199 | 0.0454583536 | -0.0531319495 |
| year2015 | 0.1957491799 | 0.1477868125 | -0.0066628319 | -0.0654791553 |
| year2016 | 0.2717881343 | 0.2045488276 | 0.0533385081 | -0.0420100906 |
| year2017 | 0.3059545102 | 0.2510745771 | -0.0126344565 | -0.0959293826 |
| year2018 | 0.1046478886 | 0.0660511420 | -0.1440933654 | -0.2512387463 |
| year2019 | 0.0724293635 | 0.0330315736 | -0.1096389733 | -0.2577367577 |
Source: Created by the authors.
Code
dplyr::mutate(data, year = factor(year, ordered = FALSE)) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam_misfs(
gam_models = maper_gam_6_by_misfs,
type = 6,
x_label = "Years",
y_label = "Predicted probability of MAPER"
)maper_gam_6_by_misfs model. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
dplyr::mutate(data, year = factor(year, ordered = FALSE)) |>
summarise_gam_misfs(mpepr_gam_6_by_misfs)
#>
#> ── Model A ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(31.103)
#> Link function: logit
#>
#> Formula:
#> mpepr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.62582314 0.03381049 -107.23960 < 2.22e-16 ***
#> year2009 0.03709332 0.04678136 0.79291 0.42783140
#> year2010 0.19467109 0.04598557 4.23331 0.000023027810392995 ***
#> year2011 0.17097103 0.04605697 3.71216 0.00020549 ***
#> year2012 0.10822804 0.04638477 2.33327 0.01963416 *
#> year2013 0.25702475 0.04560643 5.63571 0.000000017433585354 ***
#> year2014 0.16856564 0.04600552 3.66403 0.00024828 ***
#> year2015 0.34169192 0.04514264 7.56916 0.000000000000037564 ***
#> year2016 0.32731720 0.04530662 7.22449 0.000000000000502985 ***
#> year2017 0.39819008 0.04495368 8.85779 < 2.22e-16 ***
#> year2018 0.31330313 0.04537902 6.90414 0.000000000005050802 ***
#> year2019 0.17679795 0.04598024 3.84509 0.00012051 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = -0.0362 Deviance explained = 2.05%
#> -REML = -19442 Scale est. = 1 n = 7934
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 1.947212870e+4
#> 3 AIC -3.891825739e+4
#> 4 BIC -3.882753153e+4
#> 5 deviance 8.411778743e+3
#> 6 df.residual 7.922 e+3
#> 7 nobs 7.93400 e+3
#> 8 adj.r.squared -3.620918501e-2
#> 9 npar 1.2 e+1
#>
#> ── Model B ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(25.906)
#> Link function: logit
#>
#> Formula:
#> mpepr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.87698948 0.01801987 -215.15081 < 2.22e-16 ***
#> year2009 0.10877974 0.02499283 4.35244 1.3463e-05 ***
#> year2010 0.15731129 0.02484095 6.33274 2.4084e-10 ***
#> year2011 0.08050945 0.02503152 3.21632 0.0012984 **
#> year2012 0.04868841 0.02510033 1.93975 0.0524099 .
#> year2013 0.05472442 0.02534252 2.15939 0.0308198 *
#> year2014 0.07020751 0.02530395 2.77457 0.0055275 **
#> year2015 0.14517931 0.02502139 5.80221 6.5447e-09 ***
#> year2016 0.25393209 0.02470121 10.28015 < 2.22e-16 ***
#> year2017 0.37762169 0.02444039 15.45073 < 2.22e-16 ***
#> year2018 0.20054394 0.02471163 8.11537 4.8433e-16 ***
#> year2019 0.15884431 0.02473039 6.42304 1.3358e-10 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = -0.00743 Deviance explained = 1.15%
#> -REML = -90887 Scale est. = 1 n = 31734
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 9.092481949e+4
#> 3 AIC -1.818236390e+5
#> 4 BIC -1.817148921e+5
#> 5 deviance 3.487532075e+4
#> 6 df.residual 3.1722 e+4
#> 7 nobs 3.1734 e+4
#> 8 adj.r.squared -7.427616944e-3
#> 9 npar 1.2 e+1
#>
#> ── Model C ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(87.973)
#> Link function: logit
#>
#> Formula:
#> mpepr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.371412963 0.013565837 -248.52229 < 2.22e-16 ***
#> year2009 0.025612204 0.018876649 1.35682 0.17483858
#> year2010 0.089615821 0.018687209 4.79557 0.000001622127 ***
#> year2011 0.094320584 0.018645222 5.05870 0.000000422124 ***
#> year2012 0.100801844 0.018552323 5.43338 0.000000055296 ***
#> year2013 0.073971800 0.018754045 3.94431 0.000080029524 ***
#> year2014 0.029271255 0.018869216 1.55127 0.12083690
#> year2015 0.054841548 0.018767180 2.92221 0.00347563 **
#> year2016 0.070027834 0.018681384 3.74854 0.00017787 ***
#> year2017 0.019208516 0.018893706 1.01666 0.30931416
#> year2018 0.001710287 0.019054804 0.08976 0.92848093
#> year2019 -0.053550519 0.019166898 -2.79391 0.00520755 **
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = 0.00809 Deviance explained = 0.688%
#> -REML = -53470 Scale est. = 1 n = 20324
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 8.093105311e-3 very weak (negligible) cohen1988
#> 2 SE 1.251639090e-3 <NA> <NA>
#> 3 Lower CI 5.639937773e-3 very weak (negligible) cohen1988
#> 4 Upper CI 1.054627285e-2 very weak (negligible) cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 5.351150485e+4
#> 3 AIC -1.069970097e+5
#> 4 BIC -1.068940554e+5
#> 5 deviance 2.017974368e+4
#> 6 df.residual 2.03120000 e+4
#> 7 nobs 2.0324 e+4
#> 8 adj.r.squared 8.093105311e-3
#> 9 npar 1.2 e+1
#>
#> ── Model D ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(117.623)
#> Link function: logit
#>
#> Formula:
#> mpepr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.32141304 0.03214613 -103.32232 < 2e-16 ***
#> year2009 0.05759784 0.04445372 1.29568 0.195085
#> year2010 0.05320486 0.04426187 1.20205 0.229345
#> year2011 -0.06310094 0.04528226 -1.39350 0.163468
#> year2012 0.03727906 0.04439777 0.83966 0.401099
#> year2013 0.08400974 0.04387130 1.91491 0.055504 .
#> year2014 0.02121784 0.04444479 0.47740 0.633079
#> year2015 0.01473267 0.04441036 0.33174 0.740086
#> year2016 0.03800192 0.04430125 0.85781 0.390999
#> year2017 -0.02280729 0.04487438 -0.50825 0.611280
#> year2018 -0.08232164 0.04555579 -1.80705 0.070754 .
#> year2019 -0.08903243 0.04571826 -1.94742 0.051485 .
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = 0.00546 Deviance explained = 1.33%
#> -REML = -7566.8 Scale est. = 1 n = 2770
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 5.458795517e-3 very weak (negligible) cohen1988
#> 2 SE 2.788769371e-3 <NA> <NA>
#> 3 Lower CI -7.092011279e-6 no effect cohen1988
#> 4 Upper CI 1.092468305e-2 very weak (negligible) cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 7.597365316e+3
#> 3 AIC -1.516873063e+4
#> 4 BIC -1.509168480e+4
#> 5 deviance 2.718494668e+3
#> 6 df.residual 2.758 e+3
#> 7 nobs 2.77 e+3
#> 8 adj.r.squared 5.458795517e-3
#> 9 npar 1.2 e+1Code
mpepr_gam_6_by_misfs |>
summarise_coefs_misfs() |>
md_named_tibble()mpepr_gam_6_by_misfs model.
| A | B | C | D | |
|---|---|---|---|---|
| [Mean] | -0.0943307491 | -0.1850539438 | -0.2387984823 | -0.2727192850 |
| (Intercept) | -3.6258231393 | -3.8769894763 | -3.3714129630 | -3.3214130378 |
| year2009 | 0.0370933154 | 0.1087797385 | 0.0256122042 | 0.0575978433 |
| year2010 | 0.1946710948 | 0.1573112884 | 0.0896158214 | 0.0532048557 |
| year2011 | 0.1709710272 | 0.0805094531 | 0.0943205838 | -0.0631009415 |
| year2012 | 0.1082280369 | 0.0486884117 | 0.1008018444 | 0.0372790615 |
| year2013 | 0.2570247511 | 0.0547244181 | 0.0739717996 | 0.0840097367 |
| year2014 | 0.1685656423 | 0.0702075082 | 0.0292712554 | 0.0212178384 |
| year2015 | 0.3416919159 | 0.1451793123 | 0.0548415480 | 0.0147326707 |
| year2016 | 0.3273172011 | 0.2539320903 | 0.0700278339 | 0.0380019201 |
| year2017 | 0.3981900819 | 0.3776216889 | 0.0192085160 | -0.0228072923 |
| year2018 | 0.3133031313 | 0.2005439360 | 0.0017102875 | -0.0823216449 |
| year2019 | 0.1767979519 | 0.1588443050 | -0.0535505189 | -0.0890324293 |
Source: Created by the authors.
Code
dplyr::mutate(data, year = factor(year, ordered = FALSE)) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam_misfs(
gam_models = mpepr_gam_6_by_misfs,
type = 6,
x_label = "Years",
y_label = "Predicted probability of MPEPR"
)mpepr_gam_6_by_misfs model. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
dplyr::mutate(data, year = factor(year, ordered = FALSE)) |>
summarise_gam_misfs(maper_mpepr_gam_6_by_misfs)
#>
#> ── Model A ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(23.539)
#> Link function: logit
#>
#> Formula:
#> maper_mpepr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.863762847 0.030416313 -94.15220 < 2.22e-16 ***
#> year2009 0.002530356 0.042231157 0.05992 0.9522219
#> year2010 0.163563687 0.041353669 3.95524 0.0000764578584 ***
#> year2011 0.124535353 0.041518057 2.99955 0.0027038 **
#> year2012 0.107157267 0.041625158 2.57434 0.0100432 *
#> year2013 0.200257644 0.041103161 4.87207 0.0000011043276 ***
#> year2014 0.163105950 0.041256803 3.95343 0.0000770382914 ***
#> year2015 0.188558211 0.041136809 4.58369 0.0000045685023 ***
#> year2016 0.213264848 0.041090556 5.19012 0.0000002101605 ***
#> year2017 0.237457486 0.040977146 5.79488 0.0000000068372 ***
#> year2018 0.084345817 0.041776517 2.01898 0.0434896 *
#> year2019 0.005959200 0.042106384 0.14153 0.8874534
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = -0.0105 Deviance explained = 1.21%
#> -REML = -14641 Scale est. = 1 n = 7934
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 1.467225123e+4
#> 3 AIC -2.931850246e+4
#> 4 BIC -2.922777659e+4
#> 5 deviance 8.012581771e+3
#> 6 df.residual 7.922 e+3
#> 7 nobs 7.93400 e+3
#> 8 adj.r.squared -1.046017779e-2
#> 9 npar 1.2 e+1
#>
#> ── Model B ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(18.318)
#> Link function: logit
#>
#> Formula:
#> maper_mpepr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.22294516 0.01732431 -186.03595 < 2.22e-16 ***
#> year2009 0.11971504 0.02395965 4.99653 0.00000058372166 ***
#> year2010 0.15009620 0.02383549 6.29717 0.00000000030312 ***
#> year2011 0.03535440 0.02412842 1.46526 0.142850
#> year2012 0.02856854 0.02415370 1.18278 0.236896
#> year2013 0.03868681 0.02437592 1.58709 0.112492
#> year2014 0.05914037 0.02432167 2.43159 0.015033 *
#> year2015 0.09944464 0.02409824 4.12663 0.00003681107791 ***
#> year2016 0.20107932 0.02377157 8.45882 < 2.22e-16 ***
#> year2017 0.31640490 0.02350747 13.45976 < 2.22e-16 ***
#> year2018 0.08533299 0.02393219 3.56562 0.000363 ***
#> year2019 0.04507955 0.02395628 1.88174 0.059871 .
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = -0.00293 Deviance explained = 0.958%
#> -REML = -69447 Scale est. = 1 n = 31734
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 0 no effect cohen1988
#> 2 SE 0 <NA> <NA>
#> 3 Lower CI 0 no effect cohen1988
#> 4 Upper CI 0 no effect cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 6.948485640e+4
#> 3 AIC -1.389437128e+5
#> 4 BIC -1.388349659e+5
#> 5 deviance 3.380460192e+4
#> 6 df.residual 3.1722 e+4
#> 7 nobs 3.1734 e+4
#> 8 adj.r.squared -2.933590148e-3
#> 9 npar 1.2 e+1
#>
#> ── Model C ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(47.029)
#> Link function: logit
#>
#> Formula:
#> maper_mpepr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.60735423 0.01328347 -196.28559 < 2.22e-16 ***
#> year2009 0.02135162 0.01850311 1.15395 0.24852164
#> year2010 0.04981589 0.01844381 2.70095 0.00691407 **
#> year2011 0.04486920 0.01843335 2.43413 0.01492754 *
#> year2012 0.01463898 0.01845685 0.79315 0.42769265
#> year2013 0.02003883 0.01855254 1.08011 0.28009207
#> year2014 -0.03307472 0.01868558 -1.77007 0.07671606 .
#> year2015 -0.04951833 0.01872640 -2.64431 0.00818587 **
#> year2016 -0.01531973 0.01857922 -0.82456 0.40962004
#> year2017 -0.06723362 0.01878823 -3.57850 0.00034558 ***
#> year2018 -0.15569399 0.01919680 -8.11041 5.0449e-16 ***
#> year2019 -0.15251919 0.01909421 -7.98772 1.3746e-15 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = 0.0206 Deviance explained = 1.49%
#> -REML = -40563 Scale est. = 1 n = 20324
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 2.062532839e-2 weak cohen1988
#> 2 SE 1.972876581e-3 <NA> <NA>
#> 3 Lower CI 1.675856135e-2 very weak (negligible) cohen1988
#> 4 Upper CI 2.449209544e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 4.060348116e+4
#> 3 AIC -8.118096232e+4
#> 4 BIC -8.107800807e+4
#> 5 deviance 1.989046593e+4
#> 6 df.residual 2.03120000 e+4
#> 7 nobs 2.0324 e+4
#> 8 adj.r.squared 2.062532839e-2
#> 9 npar 1.2 e+1
#>
#> ── Model D ──────────────────────────────────────────────────────────────────
#>
#> Family: Beta regression(61.083)
#> Link function: logit
#>
#> Formula:
#> maper_mpepr ~ year
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -2.62777080 0.03269868 -80.36322 < 2.22e-16 ***
#> year2009 0.03742959 0.04542070 0.82406 0.409903
#> year2010 0.01671577 0.04535227 0.36858 0.712444
#> year2011 -0.09893826 0.04632765 -2.13562 0.032710 *
#> year2012 -0.02434035 0.04569124 -0.53271 0.594232
#> year2013 0.02536456 0.04514336 0.56187 0.574207
#> year2014 -0.04734035 0.04578803 -1.03390 0.301182
#> year2015 -0.05697712 0.04577360 -1.24476 0.213220
#> year2016 -0.03688130 0.04570034 -0.80702 0.419652
#> year2017 -0.08763337 0.04617991 -1.89765 0.057742 .
#> year2018 -0.20504775 0.04738514 -4.32726 0.000015098 ***
#> year2019 -0.20485571 0.04749209 -4.31347 0.000016071 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> R-sq.(adj) = 0.0212 Deviance explained = 2.44%
#> -REML = -5872.4 Scale est. = 1 n = 2770
#>
#> # A tibble: 4 × 4
#> name value interpretation rule
#> <chr> <dbl> <chr> <chr>
#> 1 R2 2.117818155e-2 weak cohen1988
#> 2 SE 5.406166049e-3 <NA> <NA>
#> 3 Lower CI 1.058229080e-2 very weak (negligible) cohen1988
#> 4 Upper CI 3.177407230e-2 weak cohen1988
#>
#> # A tibble: 9 × 2
#> name value
#> <chr> <dbl>
#> 1 df 1.200000000e+1
#> 2 logLik 5.902573955e+3
#> 3 AIC -1.177914791e+4
#> 4 BIC -1.170210208e+4
#> 5 deviance 2.706397613e+3
#> 6 df.residual 2.758000000e+3
#> 7 nobs 2.77 e+3
#> 8 adj.r.squared 2.117818155e-2
#> 9 npar 1.2 e+1Code
maper_mpepr_gam_6_by_misfs |>
summarise_coefs_misfs() |>
md_named_tibble()maper_mpepr_gam_6_by_misfs model.
| A | B | C | D | |
|---|---|---|---|---|
| [Mean] | -0.1144189191 | -0.1703368677 | -0.2441666065 | -0.2758562571 |
| (Intercept) | -2.8637628473 | -3.2229451649 | -2.6073542309 | -2.6277708030 |
| year2009 | 0.0025303559 | 0.1197150374 | 0.0213516239 | 0.0374295883 |
| year2010 | 0.1635636871 | 0.1500961951 | 0.0498158925 | 0.0167157667 |
| year2011 | 0.1245353533 | 0.0353543990 | 0.0448692036 | -0.0989382579 |
| year2012 | 0.1071572667 | 0.0285685438 | 0.0146389834 | -0.0243403455 |
| year2013 | 0.2002576435 | 0.0386868122 | 0.0200388270 | 0.0253645642 |
| year2014 | 0.1631059500 | 0.0591403696 | -0.0330747248 | -0.0473403461 |
| year2015 | 0.1885582114 | 0.0994446436 | -0.0495183316 | -0.0569771236 |
| year2016 | 0.2132648477 | 0.2010793199 | -0.0153197277 | -0.0368812975 |
| year2017 | 0.2374574859 | 0.3164048959 | -0.0672336169 | -0.0876333747 |
| year2018 | 0.0843458166 | 0.0853329872 | -0.1556939854 | -0.2050477495 |
| year2019 | 0.0059592005 | 0.0450795489 | -0.1525191913 | -0.2048557068 |
Source: Created by the authors.
Code
dplyr::mutate(data, year = factor(year, ordered = FALSE)) |>
dplyr::mutate(
dplyr::across(
.cols = dplyr::matches("^year$"),
.fns = ~ .x |> as.character() |> as.numeric()
)
) |>
plot_gam_misfs(
gam_models = maper_mpepr_gam_6_by_misfs,
type = 6,
x_label = "Years",
y_label = "Predicted probability of MAPER & MPEPR"
)maper_mpepr_gam_6_by_misfs model. Shaded areas indicates the pointwise 95% prediction confidence interval, while the faded dots in the background represent the observed data.
Acknowledgments
This analysis is part of the Sustentarea Research and Extension Group’s project: Global syndemic: the impact of anthropogenic climate change on the health and nutrition of children under five years old attended by Brazil’s public health system (SUS).
This research was supported by the Conselho Nacional de Desenvolvimento Científico e Tecnológico - Brazil (CNPq).
How to Cite
To cite this work, please use the following format:
Magalhães, A. R., Vartanian, D, & Carvalho, A. M. (2025). Global syndemic project data analysis: Report 3: Exploring potential associations between childhood undernutrition and the Standardized Precipitation Evapotranspiration Index (SPEI) in Brazilian municipalities (2008–2019). Sustentarea Research and Extension Group at the University of São Paulo. https://sustentarea.github.io/gs-data-analysis-report-3
A BibTeX entry for LaTeX users is
@techreport{magalhaes2025,
title = {Global syndemic project data analysis: Report 3: Exploring potential associations between childhood undernutrition and the Standardized Precipitation Evapotranspiration Index (SPEI) in Brazilian municipalities (2008–2019)},
author = {{Arthur Ramalho Magalhães} and {Daniel Vartanian} and {Aline Martins de Carvalho}},
year = {2025},
address = {São Paulo},
institution = {Sustentarea Research and Extension Group at the University of São Paulo},
langid = {en},
url = {https://sustentarea.github.io/gs-data-analysis-report-3}
}





























































































































































































































































